Department of Physics • University of Cologne

I will review the recent findings in the dynamics of one dimensional fluids close to integrability, which are described at large scale by a generalised form of hydrodynamics. In particular, I will present the emergence of anomalous super-diffusive transport in spin chains, the fall and rise of hydrodynamics due to turbulence effects and the interplay of hydrodynamics and quantum fluctuations.

Hyperbolic billiard motion is the canonical example of classical and quantum chaos. However, if the billiard domain has certain arithmetic properties, the resulting quantum chaos is quite different and exhibits features that are more typical of integrable systems. I will review some of these features, which have connections to deep concepts from number theory. I will then explain how such arithmetic quantum chaotic systems arise naturally inside black holes, as the interior singularity is approached.

When measured, a quantum system is subject to an unavoidable back-action, which makes the system evolve along stochastic quantum trajectories. Combined with unitary dynamics, this can lead to localization effects, like the quantum Zeno effect, and to the stabilization of new out-of-equilibrium steady-state in many-body systems. The recent characterization of these phases has shown that the universal properties of their phase transitions differ between individual quantum trajectories and their statistical ensemble. In this talk, I will review the description of quantum measurements and their back action in their discrete and continuous framework. I will first revisit the Zeno effect along individual (post-selected) trajectories and their statistical ensemble in an exactly solved single-qubit model. I will then extend the considerations to many-body systems and their measurement-induced phase transitions (MiPTs) and introduce a theory of partial post-selection, in which we restrict the stochastic dynamics to a controllable subset of quantum trajectories. Focusing on a Gaussian Majorana fermions model, I will show that the MiPT universality of the post-selected (single-trajectory) dynamics is stable against the inclusion of stochasticity from a small subset of quantum trajectories, but the monitored limit belongs to a different universality class. Our results provide a systematic way to study trajectory-averaged measurement-induced effects.

In photonic systems, gain and loss can be used to induce intriguing effects that are linked to non-Hermitian and topological physics. Prominent examples are exceptional points and the non-Hermitian skin effect, which can be used for enhanced sensing and directed amplification, as well as symmetry-protected states, which can be addressed by topological mode selection. Many of these applications make explicit use of mode nonorthogonality, which becomes especially interesting when the system is nonreciprocal. I describe how these effects can be probed in response theory, transport, and scattering, and highlight fundamental practical limits of the observability of some effects.

Fractals — objects with non-integer dimensions — occur in manifold settings and length scales in nature, ranging from snowflakes and lightning strikes to natural coastlines. Much effort has been expended to generate and study fractals in many-body physics, oftentimes underpinned by the presence of disorder. Here, we identify an emergent dynamical fractal in a disorder-free, stoichiometric three-dimensional magnetic crystal in thermodynamic equilibrium. The phenomenon is borne out of constraints on the dynamics of the microscopic degrees of freedom imposed by the topological nature of the system and by its characteristic point-like excitations, which at low temperatures become restricted to move on the fractal. This observation explains the anomalous exponent found in magnetic noise experiments on Dy2Ti2O7, and it resolves a long standing puzzle about its rapidly diverging relaxation time. This is a case in point of the capacity of even simple topological many-body systems to exhibit striking phenomena in their cooperative dynamics, and of the promise they hold for further surprising discoveries.

Repeated projective measurements in unitary circuits can lead to an entanglement phase transition as the measurement rate is tuned. In this work, we consider a different setting in which the projective measurements are replaced by dynamically chosen unitary gates that minimize the entanglement. This can be seen as a one-dimensional unitary circuit game in which two players get to place unitary gates on randomly assigned bonds at different rates: The “entangler” applies a random local unitary gate with the aim of generating extensive (volume law) entanglement. The “disentangler”, based on limited knowledge about the state, chooses a unitary gate to reduce the entanglement entropy on the assigned bond with the goal of limiting to only finite (area law) entanglement. In order to elucidate the resulting entanglement dynamics, we consider three different scenarios: (i) a classical discrete height model, (ii) a Clifford circuit, and (iii) a general Haar random unitary circuit. We find that both the classical and Clifford circuit models exhibit phase transitions as a function of the rate that the disentangler places a gate, which have similar properties that can be understood through a connection to the stochastic Fredkin chain. In contrast, the “entangler” always wins when using Haar random unitary gates and we observe extensive, volume law entanglement for all non-zero rates of entangling.

Describing strongly interacting electrons is one of the crucial challenges of modern quantum physics. A comprehensive solution to this electron correlation problem would simultaneously exploit both the pairwise interaction and its spatial decay. By taking a quantum information perspective, we explain how this structure of realistic Hamiltonians gives rise to two conceptually different notions of correlation and entanglement. The first one describes correlations between orbitals while the second one refers more to the particle picture. We illustrate those two concepts of orbital and particle correlation and present measures thereof. Our results for different molecular systems reveal that the total correlation between molecular orbitals is mainly classical, raising questions about the general significance of entanglement in chemical bonding. Finally, we also speculate on a promising relation between orbital and particle correlation and explain why this may replace the obscure but widely used concept of static and dynamic correlation.

Quantum oscillation phenomena describe the periodic variation of thermodynamic and transport properties of materials as a function of magnetic field. Since their discovery in 1930, their observation is commonly assumed to be a definite sign for the presence of a Fermi surface (FS) in a metal. Indeed, the effect forms the basis of a well-established experimental procedure for accurately measuring FS topology and geometry of metallic systems. In this talk I will discuss recent developments which challenge the canonical description of quantum oscillations. I will first review our work on quantum oscillations in insulators. Next, I will discuss the possibility of sharp quantum oscillation frequencies in metals which do not correspond to Fermi surface orbits and the effect of strong electron interactions. Finally, I will present experimental results confirming our theoretical predictions and discuss the broader implications of anomalous quantum oscillations.

After a general introduction in dynamical density functional theory (DDFT) we show that this theory provides a versatile tool to describe bacterial colonies. We formulate the growth and division of bacteria within a DDFT framework and include the effect of dynamical mechano-self-regulation of cell size. Theoretical predictions are compared to particle-resolved computer simulations and to experiments. The theory is generalizable to binary systems as well.

The Mpemba effect is the counterintuitive and controversial phenomenon that hot water cools faster than cold one. Here I will introduce an analogous effect recently proposed and observed in extended quantum systems in which a symmetry is explicitly broken by the initial state, but it is restored by the time evolution. To study this phenomenon we introduce a new quantity, dubbed entanglement asymmetry, which is a measure of symmetry breaking inspired by the theory of entanglement in many-body states.

The field of quantum annealing is undergoing a rapid development in terms of its application to quantum simulations. In this talk, I will first give an overview of quantum annealing with some emphasis on real-world applications. I then describe our recent work on coherent quantum simulation to experimentally test the Kibble-Zurek mechanism for the 1d transverse-field Ising model [1]. [1] A. King et al, Nature Phys. 18, 1324 (2022) https://www.nature.com/articles/s41567-022-01741-6

In the NISQ era, we are looking to approach quantum advantage with shallow algorithms, which are often variational in nature. In those cases, proofs of speedup are hard to come by and a lot of research is empirical. A particularily relevant case here is the Quantum Approximate Optimization Algorithm (QAOA). I will present its semiclassical limit, mean-field QAOA, which can be classically simulated and present a criterion for its applicability, hence allowing to identify cases when full QAOA is not promising. Another relevant case is the study of quantum manybody systems with digital algorithms. Here, I will show an improved, physics-inspired algorithm to sample the key observable for studying theses systems, the single-particle Green’s function. Work with Dmitry Bagrets, Aditi Misra-Spieldenner, Tobias Stollenwerk, Tim Bode, Peter Schuhmacher, David Headley, and Gino Bishop

Memory formation and ageing are abundant in many soft matter systems. The disorder underlying these systems gives rise to a rich energy landscape, consisting of a large number of metastable states. These landscapes are accompanied by a plethora of pathways, along which such systems can evolve when exposed to a varying temperature or mechanical load. The resulting dynamics can be rather complex, giving rise to dynamically critical phenomena such as irreversibility and yielding. At the same time, such system exhibit parallels with the adaptive evolution of biological populations in time-varying environments. In this talk I will present a general framework to analyze the dynamics and memory formation of driven disordered systems. I will then show how this framework can be applied to understand both the response of a cyclically sheared amorphous solid, as well as the antibiotic resistance evolution of a microbial population subject to time-varying drug concentrations.

We prove a generic spin-statistics relation for the fractional quasiparticles that appear in quantum Hall planar setups. The proof is based on an efficient way for computing the Berry phase acquired by a generic quasiparticle translated in the plane along a circular path, and on the crucial fact that once the gauge-invariant generator of rotations is projected onto a Landau level, it fractionalizes among the quasiparticles and the edge. Using these results we define a measurable quasiparticle fractional spin that satisfies the spin-statistics relation. As an application, we predict the value of the spin of the composite-fermion quasielectron proposed by Jain; our numerical simulations agree with that value. We also show that the difficulties encountered when studying the statistical properties of Laughlin’s quasielectron can be traced back to a spin that does not satisfy the spin- statistics relation. We conclude with some remarks on the total angular momentum of the system as a function of the quasiparticle positions and on an ambiguity in the definition of the spin. Further results on the non-Abelian anyons of the Moore-Read wavefunction will be presented. References [1] A. Nardin, E. Ardonne and LM, unpublished [2] Comparin, Biella, Opler, Macaluso, Polychronakos, LM, PRB 105 085125 (2022) [3] Macaluso, Comparin, LM, Carusotto, PRL 123 266801 (2020)

Active matter is matter driven out of equilibrium by its microscopic constituents. Common examples include the cytoskeleton of the cell, bacteria swimming in a fluid, or herds of wildebeest on the African planes. In these systems, the constituents create forces and motion driving the system out of equilibrium. But now imagine cells dividing or a tumor growing. Then activity does not enter the dynamics via the forces, but by material conservation. The material generates itself. In order to grow, cells must exert mechanical pressure on the neighboring tissue. In turn, mechanical stress influences growth and may play a role in cell competition. This insight has led to the notion of homeostatic pressure – the pressure exerted by a tissue in homeostasis. We use particle based computer simulations to model growing tissues. Surprisingly, we find that when cross interactions are taken into account tissues with different homeostatic pressure can coexist and the evolution can favor the weaker tissue, or even results in tumor heterogeneity.

There are few candidates for quantum algorithms which might outperform classical approaches while being amenable to noisy quantum computing devices. Beside quantum simulation algorithms, quantum algorithms for approximate optimization are promising candidates. The target application for these approaches is finding approximate solutions to combinatorial optimization problems. In this talk I will give an overview on quantum approximate optimization approaches, while mainly focusing on the quantum approximate optimization algorithm (QAOA), quantum annealing and variations thereof. I will demonstrate these concepts by considering a particular real-world planning problem, the flight-gate assignment problem [1]. In addition, I will cover novel approaches for the diagrammatic analysis of parametrized quantum circuits, like QAOA. Here I will demonstrate how such methods can be employed to help with the performance investigation of QAOA and other variational quantum algorithms. [1] https://ieeexplore.ieee.org/document/9222273 [2] https://arxiv.org/abs/2204.01307

Several lattice models display a condensation transition in real space when the density of a suitable order parameter exceeds a critical value. At equilibrium there are well established results and we discuss different scenarios of the condensation transition. In the out-of-equilibrium setup we consider one of such model with two conservation laws, attached to two external reservoirs, R_1 and R_2. Both reservoirs impose subcritical boundary conditions: When R_1=R_2 the system is in equilibrium below the localization threshold and no condensate appears. Instead, when R_1 differs from R_2 localization may arise in an internal portion of the lattice. This phenomenon is due to the coupled transport of two conserved quantities. In collaboration with Gabriele Gotti and Stefano Iubini.

We review some recent results on the development of efficient unconstrained tree tensor network algorithms and their applications to high-dimensional many-body quantum systems and machine learning problems in High Energy Physics. In particular, we present results on topological two-dimensional systems, two dimensional Rydberg atom systems, and two and three-dimensional lattice gauge theories in presence of fermonic matter. Finally, we present their application to LHCb event classification and to the study of open many-body quantum systems, specifically to the computation of the entanglement of formation in critical many-body quantum systems at finite temperature.

Laser-induced optical excitation of hydrogen-like alkaline and alkalineearth atoms can be used to create arrays of highly controllable Rydberg states, which are promising candidates for atom-based quantum computation and for realizing new many-body phenomena. In a gas of atoms, the interplay between the laser-drive and strong interactions between Rydberg states yields new cooperative effects, including either the complete blocking or the facilitation of excitations by a nearby Rydberg state. I will discuss theoretical and experimental approaches to the so-called facilitation regime, in which the creation of excitations is conditioned on the presence of a nearby Rydberg state. This gives rise to a kinetically constrained dynamics, supporting the avalanche-like spreading of excitations and a non-equilibrium phase transition into an absorbing state with zero excitations. The interplay of interactions, laserdrive, dissipation and atomic motion, each acting on their individual timescale, gives rise to a multifaceted dynamics. It ranges from an epidemiclike spreading of excitations on an emergent complex network at short times to a long-lived critical regime of repeated scale invariant excitation avalanches, reminiscent of self-organized criticality, at late times.

A theory for the nonlocal shear stress correlations in supercooled liquids and colloidal suspensions is derived from first principles. It captures the crossover from viscous to elastic dynamics at an idealized liquid to glass transition and explains the emergence of long-ranged stress correlations in glass, as expected from classical continuum elasticity. Whereas Eshelby‘s elasticity pattern is recovered independently of the dynamics, the Goldstone modes differ drastically: Newtonian dynamics leads to propagating transverse sound, while the Goldstone modes of a colloidal glass are diffusive. Precursors of the long-ranged anisotropic stress correlations in the fluid can be observed in both cases. Their spatial extent can be characterized by a correlation length, which grows like the shear viscosity for a Newtonian fluid and like its square root in a colloidal fluid. These results are derived within a hydrodynamic theory, generalising Maxwell‘s model to finite wavenumbers, after the dynamics has been decomposed into potentially slow modes, associated with conservation laws and/or the order parameter, and fast microscopic degrees of freedom.

Quantum systems are generally extremely hard to isolate from their environment, even more so if we want to exert control or perform measurements. It is therefore important to understand the effect of the coupling to the environment. I will discuss a random matrix approach to quantum many-body systems with strong dissipation and show that the locality of dissipation processes gives rise to a hierarchy of relaxation timescales, which can be experimentally observed. This theory can also be applied to the case of a strong variance in dissipation strengths, which can lead to an emerging set of metastable states.

A record is an entry in a time series that is greater or smaller than all previous entries. The public perception of climate change is particularly sensitive to record-breaking weather events, which often receive extensive media coverage. As a consequence, a number of recent studies have been aimed at detecting and quantifying the effects of a warming climate on the frequency of temperature records. The mathematical theory of records makes universal and sometimes counter-intuitive predictions about the temporal statistics of record events, but it is largely restricted to stationary time series. After an introduction to the classic theory, I will explain the extensions needed to deal with trends, and the effect of warming on temperature records will be described at different levels of resolution. In the last part of the talk I will discuss time series of precipitation records, where the presence of dry days of zero precipitation induces nontrivial correlations between record-breaking events.

This talk includes two works that have relation to the Kitaev model on the honeycomb lattice. In the first part, I will focus on the properties of the spin-1 Kitaev model, and discuss the controversial results about whether the spin-1 model is gapless. In the second part, I will talk about the spin-orbital generalizations of the Kitaev model, and transitions between topological phases featuring emergent fractionalized excitations. Reference: 1. Physical Review B 102, 121102 (R) (2020) 2. Physical Review Letters 125, 257202 (2020)

As physical implementations of small quantum computers become a reality, we investigate two common bottlenecks: limited memory size and noise caused by heat dissipation. In this talk I will go over the theoretical fundamentals behind heat production in quantum information processing, and how it can be alleviated without a large cost in terms of quantum memory requirements. The talk will be accessible to non-experts, familiar with quantum mechanics. Landauer posited that irreversible information-processing operations (like the erasure of a classical or quantum memory at the end of a computation) have an intrinsic thermodynamic work cost, which is associated with heat dissipation to the environment [1]. In the case of a quantum computer this heat dissipation is particularly undesirable, as the computer relies on cooling to keep coherence of quantum states. Bennett proposed a solution: if we run the circuit up until the final measurements and then reverse it, we keep heat production to a theoretical minimum [2]. However, this proposal has a cost in terms of quantum memory: none of the quantum registers that are only needed for parts of the computation can be freed until the very end. In the intermediate term, when we have only a few hundreds of qubits in a quantum memory, this is a bottleneck for parallelization of quantum computations: we have to wait to finish an algorithm before we can free the memory to run another. In recent work, we try to ameliorate this problem by investigating "online erasure" of quantum registers that are no longer needed for a given algorithm. That way, we could free up quantum memory already halfway through a computation. We study the minimal cost of erasure in these scenarios, using results on the erasure of entangled quantum registers [3]. For a specific class of algorithms (the hidden subgroup problem) we find optimal online erasure protocols, and see how we could use them to optimize the algorithms [4].

Topological phases were discovered in condensed matter physics and recently extended to classical physics such as topological mechanical metamaterials. Their study and realization in soft-matter and biological systems has only started to develop. In this talk we discuss how topological phases may determine the behavior of nonlinear dynamical systems that arise, for example, in population dynamics. We have shown that topological phases can be realized with the anti-symmetric Lotka-Volterra equation (ALVE). The ALVE is a paradigmatic model system in population dynamics and governs, for example, the evolutionary dynamics of zero-sum games, such as the rock-paper-scissors game [1], but also describes the condensation of non-interacting bosons in driven-dissipative set-ups [2]. We have shown that for the ALVE, defined on a one-dimensional chain of rock-paper-scissors cycles, robust polarization emerges at the chain’s edge [3]. The system undergoes a transition from left to right polarization as the control parameter passes through a critical value. At the critical point, solitary waves are observed. We found that the polarization states are topological phases and that this transition is indeed a topological phase transition. Remarkably, this phase transition falls into symmetry class D within the “ten-fold way” classification scheme of gapped free-fermion systems, which also applies, for example, to one-dimensional topological superconductors. Beyond the observation of topological phases in the ALVE, it might be possible to generalize the approach of our work to other dynamical systems in biological physics whose attractors are nonlinear oscillators or limit cycles. [1] J. Knebel, T. Krüger, M. F. Weber, and E. Frey, Phys. Rev. Lett. 110, 168106 (2013). [2] J. Knebel, M. F. Weber, T. Krüger, and E. Frey, Nature Communications 6, 6977 (2015). [3] J. Knebel, P. M. Geiger, and E. Frey, Phys. Rev. Lett. (in press) [arXiv:2009.01780].

Quantum Simulation promises insight into quantum physics problems which are beyond the ability to calculate with conventional methods. Quantum simulators can be built either using a ‘digital’ Trotter decomposition of the problem or by directly building the Hamiltonian in the lab and performing ‘analogue’ experiments. I will present here a different approach, by which the model to simulate emerges naturally from a completely different microscopic Hamiltonian. I will illustrate this in the example of the emergence of the Sine-Gordon quantum field theory from the microscopic description of two tunnel coupled super fluids. Special emphasis will be put on how to verify such emergent quantum simulators and how to characterize them. Thereby I will present two tools: High order correlation functions and their factorization [1], the evaluation of the quantum effective action and the momentum dependence of propagators and vertices (running couplings, renormalization of mass etc ..) of the emerging quantum field theory [2] and quantum field tomography that points to a new way to read out quantum simulators [3]. Together they establish general methods to analyse quantum systems through experiments and thus represents a crucial ingredient towards the implementation and verification of quantum simulators. Work performed in collaboration with the groups of Th. Gasenzer und J. Berges (Heidelberg), Jens Eisert (FU Berlin) and E. Demler (Harvard). Supported by the DFG-FWF: SFB ISOQUANT: and the EU: ERC-AdG QuantumRelax [1] T. Schweigler et al., Nature 545, 323 (2017), arXiv:1505.03126 [2] T. Zache et al. Phys. Rev. X 10, 011020 (2020) [3] M. Gluza et al., Communication Physics 3, 12 (2020)

In the last five years, a new field has emerged at the intersection between Condensed Matter and Quantum Optics, denominated “Quantum Magnonics”. This field strives to control the elementary excitations of magnetic materials, denominated magnons, to the level of the single quanta, and to interface them coherently to other elementary excitations such as photons or phonons. The recent developments in this field, with proof of concept experiments such as a single-magnon detector, have opened the door for hybrid quantum systems based on magnetic materials. This can allow us to explore magnetism in new ways and regimes, has the potential of unraveling quantum phenomena at unprecedented scales, and could lead to breakthroughs for quantum technologies. A predominant role in these developments is played by cavity optomagnonic systems, where an electromagnetic cavity, either in the optical or microwave regime, is used to enhance and control the interaction between photons and magnons. In this talk, I will introduce the field of Quantum Magnonics with emphasis on Cavity Optomagnonics, and present some theoretical results from our group which aim to push the boundaries of the current state of the art.

Topological quantum chemistry (TQC) framework has provided a complete description of the universal properties of all possible atomic band insulators in all space groups considering the crystalline unitary symmetries. It links the chemical and symmetry structure of a given material with its topological properties. While this formalism filled the gap between the mathematical classification and the practical diagnosis of topological materials, an obvious limitation is that it only applies to weakly interacting systems. It is an open question to which extent this formalism can be generalized to correlated systems that can exhibit symmetry protected topological Mott insulators. In this talk I will first introduce TQC and its application and then I will address this question by combining cluster perturbation theory and topological Hamiltonians within TQC. This simple formalism will be applied to calculate to the phase diagram of a representative model. The results are compared to numerically exact calculations from density matrix renormalization group and variational Monte Carlo simulations together with many-body topological invariants. References 1. M.G. Vergniory, L. Elcoro, C. Felser, N. Regnault, B.A. Bernevig, Z.Wang, “A complete catalogue of HighQuality Topological Materials“, Nature 566, 480-485 (2019) 2. B. Bradlyn, L. Elcoro, J. Cano, M.G. Vergniory, Z. Wang, C. Felser, M.I. Aroyo, B.A. Bernevig, “Topological quantum chemistry”, Nature 547 (7663), 298-305 (2017). 3. M. Iraola et al, in preparation

Novel computational paradigms in combination with proper hardware solutions are required to overcome the limitations of our state-of-the-art computer technology, in particular regarding energy consumption. Due to the inherent complex and non-linear nature, spintronics offers the possibility towards energy-efficient, non-volatile hardware solutions for various unconventional computing schemes.[1-3] In this talk, I will discuss the possibility of using magnetic skyrmions for in particular two unconventional computing schemes – reservoir computing and stochastic computing. Reservoir computing is a computational scheme that allows to simplify spatial-temporal recognition tasks. We have shown that random skyrmion fabrics provide a suitable physical implementation of the reservoir[4,5] and allow to classify patterns via their complex resistance responses either by tracing the signal over time or by a single spatially resolved measurement.[6] Stochastic computing is a computational paradigm that allows to speed up a calculation while trading for numerical precision. Information is encoded in terms of bitstreams as a probability. A key requirement and simultaneously a challenge is that the incoming bitstreams are uncorrelated. The Brownian motion of magnetic skyrmions allows creating a device that reshuffles the bit-streams.[7,8] [1] J. Grollier, D. Querlioz, K. Y. Camsari, KES, S. Fukami, M. D. Stiles, Nat. Electron. (2020) [2] E. Vedmedenko, R. Kawakami, D. Sheka, ..., KES, et al., J. of Phys. D (2020) [3] G. Finocchio, M. Di Ventra, K.Y. Camsari, KES, P. K. Amiri and Z. Zeng, arXiv:1907.04601 [4] D. Prychynenko, M. Sitte, et al, KES, Phys. Rev. Appl. 9, 014034 (2018) [5] G. Bourianoff, D. Pinna, M. Sitte and KES, AIP Adv. 8, 055602 (2018) [6] D. Pinna, G. Bourianoff and KES, arXiv:1811.12623 [7] D. Pinna, F. Abreu Araujo, J.-V. Kim, et al, Phys. Rev. Appl. 9, 064018 (2018) [8] J. Zazvorka, F. Jakobs, D. Heinze, ..., KES, et al., Nat. Nanotech. 14, 658 (2019)

While molecular gases are well described by established kinetic theories, when macroscopic granular particles replace molecules as the constituents in a granular gas, new challenges arise due to the dissipative nature of their collisions. Including dissipation into the theories leads to three main predictions: 1. non-Maxwellian velocity distributions, 2. homogeneous cooling following the algebraic Haff's law and 3. emergence of cluster instabilities. Experimental test of the theories requires (i) a low-gravity environment, and (ii) external excitation of the granular particles that can drive them into a homogeneous spatial distribution. An experiment - Magnetically Excited Granular Matter (MEGraMa) - was developed at DLR to meet these demands and flown on board of parabolic flights, in a drop tower, and on a sounding rocket. While the first two theoretical predictions can be demonstrated convincingly, quantitative deviations between theory and experiment are apparent.

In this talk I will describe how topology emerges in crystalline environments from the perspective of local orbitals and highlight subtleties which appear when characterizing topology protected by crystalline symmetry. I will introduce a new notion of a topological obstruction which is not protected by bulk energy gap closings in periodic boundary conditions, but only in systems with open boundaries, which we call boundary obstructed topological phases. We will describe in this context on a celebrated model - the quantized quadrupole insulator in two-dimensions.

Systems consisting of a large number of interacting bosons or fermions in two dimensions can in some situations form anyonic quasiparticles that are neither bosons, nor fermions. Such systems are topologically ordered, and they have many special properties. They are, for instance, not characterized by a local order parameter, which makes it challenging to detect the phases. Here, we demonstrate that anyons are an interesting tool to detect topological order in new types of systems and to detect phase transitions involving topological phases. The phase transitions are detected based on the idea that the system does not support the same types of quasiparticles on the two sides of the transition. We test the method on three rather different examples, and in all cases we find that it is sufficient to study a simple property of the anyons, requiring low numerical costs, to accurately detect the phase transition point. A further advantage of the method is that it does not require particular boundary conditions, and we utilize this to demonstrate that topological order can also occur in fractal dimensions and on quasicrystals. References: arXiv:1909.02046, arXiv:1907.03193, PRB 101, 115413 (2020).

A non-Hermitian PT-symmetric version of the kicked top is introduced to study the interplay of quantum chaos with balanced loss and gain. The classical dynamics arising from the quantum dynamics of the angular momentum expectation values are derived. It is demonstrated that the presence of PT-symmetry can lead to ''stable'' mixed regular chaotic behaviour without sinks or sources for subcritical values of the gain-loss parameter. For large values of the kicking strength a strange attractor is observed that also persists if PT-symmetry is broken. Classical structures are also identified in the quantum dynamics. Finally, some of the statistics of the eigenvalues of the quantum system are analysed.

No, we can’t. The time at which the growth in the number of infected individuals halts and starts decreasing cannot be calculated with certainty before the turning point is actually attained. This assertion is illustrated by adding to a standard SIR model a new class for confined individuals. A Bayesian fit to the on-going COVID-19 pandemic in Spain shows that a slow-down in the number of newly infected individuals during the expansion phase allows to infer neither the precise position of the maximum nor whether the measures taken will bring the propagation to the inhibition regime. Our study warns against precise forecasts of the evolution of epidemics based on mean-field, effective models, and supports that only probabilities of different outcomes can be confidently given.

This talk will describe some current efforts to track, understand, and control the current corona virus pandemic. We will review basic epidemiology and discuss the dynamics of transmissions, as well as monitoring efforts aimed to contain local outbreaks. We will also compare different scenarios of viral evolution.

Quantum systems bring unprecedented advantages to the realization of classical cryptographic tasks. A remarkable example is quantum key distribution, which allows two parties, Alice and Bob, to establish a shared secret key that can be used for unconditionally secure communication. Furthermore, the strong correlations exhibited by quantum systems can be explored to construct cryptographic protocols that are secure even when the parties are completely ignorant about the internal working of their devices. This is the device-independent paradigm. In this talk I will introduce the device-independent scenario and comment on recent results on device-independent quantum key distribution. Then I will move to the scenario of many parties and discuss multipartite cryptographic tasks. Finally, I will present new results on bounding the uncertainty of an eavesdropper in this setting, and discuss their application to multipartite cryptographic protocols.

Machine learning techniques can boost the exploration of complicated phase diagrams in many-body systems. To date, most studies are tied to situations involving only one phase transition and one order parameter. Systems accommodating multiple phases of coexisting and competing orders remain largely unexplored. Using Support Vector Machines (SVMs) we focus on multipolar orders and their tensorial order parameters, whose identification is difficult with traditional methods. The key property that allows one to make progress is the interpretability of the decision function, from which the physical order parameter can be deduced. Furthermore, we discuss a second intrinsic parameter of the SVM, the bias, which allows one to make an unsupervised graph analysis of the topology of the phase diagram. We illustrate our tool for the classical XXZ model on the frustrated pyrochlore lattice. Unexpectedly, the machine could also learn local constraints hinting at various types of spin liquids resulting in a complete classification of all types of behavior for this model.

Quantum information theory combines classical information theory with quantum physics. This combination opens the door to many fascinating applications which either do not have a classical counterpart or outperform them. Prominent examples thereof are quantum communication and quantum computation and simulations. Many of the application are possible due to the subtle properties of quantum many-body systems. In particular entanglement, which is a strong correlation among several quantum systems, plays an essential role. In this talk, I will first present some recent results on multipartite entanglement theory. In particular, I will show that deterministic local transformations among pure n-partite d-level systems are almost never possible. The consequences of these findings in the context of entanglement theory will be discussed. Then I will talk about certain aspects of quantum computations, where entanglement plays an important role. I will consider quantum algorithms which are composed of so-called matchgates. I will show that such an algorithm can always be compressed into an exponentially smaller quantum computation. However, as will be explained, the usage of an additional resource, the so-called magic states, elevates such a computation to universal quantum computation, while maintaining the same gate set. I will present the characterization of these magic states and discuss the consequences of these results in the context of quantum computation.

Graphene is one of the most versatile materials to realize exotic phenomena in condensed matter, as a consequence of the emergent Dirac dispersion at low energies. Introducing one more layer of complexity, we find bilayer graphene, which can be manipulated to achieve an arbitrary twist angle between the two layers. Twisted bilayer graphene (TBG) has recently attracted a lot of attention for the observed superconductivity and correlated electronic behavior at particular twist angles called magic angles. Here, I discuss two novel ways to control the electronic properties of twisted bilayer graphene, in particular: - Artificial gauge fields: We established that the application of a homogeneous electric field perpendicular to the bilayer is mathematically equivalent to a new kind of synthetic gauge field in the small twist angle regime. This identification opens the door for the generation and detection of pseudo-Landau levels in graphene platforms within robust setups, which do not depend on strain engineering. Furthermore, this new artificial gauge field leads to the development of highly localized modes in emergent triangular or Kagome lattices, associated with flat bands close to charge neutrality. - Triple point Fermions: These are elusive electronic excitations that generalize Dirac and Weyl modes beyond the conventional high energy paradigm. Yet, finding real materials naturally hosting these excitations at the Fermi energy has remained a challenge. In this work, we show how TBG can realize robust triple point fermions in two dimensions by the introduction of localized impurities.

Recent experiments in quantum Hall bilayer systems have revealed a new strongly correlated state: the semi-quantized quantum Hall state. This state arises in a bilayer quantum Hall system with strong interlayer-interactions, has a quantized Hall resistance and vanishing longitudinal resistance, while at the same time featuring a gapless sector that allows this state to exist for a continuum of filling factors. In this talk, I will explain what a semi-quantized quantum Hall state is, and use a coupled-wire construction to predict possible future experiments in the already existing experimental platforms.

A unified theory for space-time and matter might be based on finite projective geometries instead of differentiable manifolds and fields. Each point of the world is equipped with a quadratic form over a finite Galois field which define neighbors in the finite set of points. Due to the projective equivalence of all quadratic forms this world is necessarily a 4-dimensional, locally Lorentz-covariant space-time with a gauge symmetry G(3)xG(2)xG(1) for internal points which represent elementary particle degrees of freedom. Thus, matter appears as a geometric distortion of an inhomogeneous field of quadrics and all physical properties (spins, charges) of the standard model seem to follow from its finite geometric structure in a continuum limit. The finiteness inevitably induces a fermionic quantization of all matter fields and a bosonic for gauge fields. The main difference to Einstein's general theory of relativity is the use of finite fields instead of real numbers to parametrize points of events.

We explore the intriguing spatial patterns that emerge in a two-dimensional spatially inhomogeneous Katz-Lebowitz-Spohn (KLS) driven lattice gas with attractive nearest-neighbor interactions. The domain is split into two regions with hopping rates governed by different temperatures T > T_c and T_c, respectively, where T_c indicates the critical temperature for phase ordering, and with the temperature boundaries oriented perpendicular to the drive. In the hotter region, the system behaves like the (totally) asymmetric exclusion processes (TASEP), and experiences particle blockage in front of the interface to the critical region. To explain this particle density accumulation near the interface, we have measured the steady-state current in the KLS model at T > T_c and found it to decay as 1/T. In analogy with TASEP systems containing "slow" bonds, transport in the high-temperature subsystem is impeded by the lower current in the cooler region, which tends to set the global stationary particle current value. This blockage is induced by the extended particle clusters, growing logarithmically with system size, in the critical region. We observe the density profiles in both high-and low- temperature subsystems to be similar to the well-characterized coexistence and maximal-current phases in (T)ASEP models with open boundary conditions, which are respectively governed by hyperbolic and trigonometric tangent functions. Yet if the lower temperature is set to T_c, we detect marked fluctuation corrections to the mean-field density profiles, e.g., the corresponding critical KLS power law density decay near the interfaces into the cooler region. If the temperature interface is aligned parallel to the drive, we observe the cooler region to act as an absorbing sink for particle transport, with blockages emerging at the subsystem boundaries.

It is an open question how well tensor network states in the form of an infinite projected entangled-pair states (iPEPS) tensor network can approximate gapless quantum states of matter. In this talk we address this issue for two different physical scenarios: (i) a conformally invariant (2+1)d quantum critical point in the incarnation of the transverse-field Ising model on the square lattice and (ii) spontaneously broken continuous symmetries with gapless Goldstone modes exemplified by the S=1/2 antiferromagnetic Heisenberg and XY models on the square lattice. We find that the energetically best wave functions display finite correlation lengths and we introduce a powerful finite correlation length scaling framework for the analysis of such finite bond dimension (finite-D) iPEPS states. The framework is important (i) to understand the mild limitations of the finite-D iPEPS manifold in representing Lorentz-invariant, gapless many-body quantum states and (ii) to put forward a practical scheme in which the finite correlation length ξ(D) combined with field theory inspired formulas can be used to extrapolate the data to infinite correlation length, i.e., to the thermodynamic limit. The finite correlation length scaling framework opens the way for further exploration of quantum matter with an (expected) Lorentz-invariant, massless low-energy description, with many applications ranging from condensed matter to high-energy physics.

The Sachdev-Ye-Kitaev (SYK) model describes a system of a large number of randomly interacting Majorana fermions. It stands in the tradition of the random k-body interaction models pioneered in nuclear physics and later applied in condensed matter contexts. The SYK model can be looked at from three interrelated perspectives: a) a system showing many body chaos and random matrix correlations, b) a paradigm of strongly correlated (Majorana) quantum matter, and c) the holographic shadow of a two-dimensional AdS2 gravitational bulk. The interplay of these three has made it a focus of intensive research. Previous analytic work was restricted to the study of quantum correlations at time scales short compared to the inverse of the many body level spacing. In this talk, we address the complementary regime of large times. We will apply a matrix integral formalism to identify a set of collective modes in Fock space describing the relaxation of the system towards an ergodic long time limit. We will discuss universal signatures of these modes in spectral correlations, and compare our results to numerics. Finally, we will discuss the structure of the system’s many body wave functions and point out differences to the wave functions of chaotic single particle systems.

An infinite projected entangled pair state (iPEPS) is a variational tensor network ansatz to represent 2D ground states in the thermodynamic limit where the accuracy can be systematically controlled by the bond dimension D of the tensors. Thanks to several methodological advances in recent years, iPEPS has become a very powerful tool for the study of 2D strongly correlated systems, in particular models where quantum Monte Carlo fails due to the negative sign problem. In the first part of my talk I will report on recent progress in simulating the 2D Hubbard model, focussing on a particularly challenging point in the phase diagram, U/t=8 and 1/8 doping. A very close competition between several low-energy states is found, including a uniform d-wave superconducting state and different types of stripe states. Systematic extrapolations to the exact, infinite D limit show that the ground state is a period 8 stripe, while stripes with periods 5-7 being very close in energy. Consistent results are also obtained with density matrix embedding theory, density matrix renormalization group, and constrained-path auxiliary field quantum Monte Carlo. On the other hand, period 4 stripes - which are typically observed in experiments on the cuprates - are clearly higher in energy. However, they become energetically favored upon adding a realistic next-nearest neighbor hopping term. In the second part I will show how to systematically study 2D quantum critical phenomena with iPEPS using so-called finite correlation length scaling. This approach is very similar to conventional finite size scaling, but instead of performing the scaling analysis using different system sizes, it is done based on an effective correlation length extracted from the iPEPS. We apply this method to interacting spinless fermions on a honeycomb lattice at half filling and obtain a critical coupling and critical exponents which are in agreement with quantum Monte Carlo results.

Largely unnoticed by theoretical physics, the last 20 years have seen a revolution in nano-particle processing. One example is that powders - although very porous, when freshly produced - can be converted into a dense solid, which still keeps a microstructure at the nanoscale. The processes are new developments related to what traditionally was called "Spark Plasma Sintering", but has nothing to do with sparks and plasmas. Computer simulations predict intermediate steps of these processes and reveal the underlying mechanisms. I will give a review of recent simulations, with a focus on so-called flash-sintering.

I will discuss ways in which the quantum world is different from the classical world, and how these differences might be used to design quantum computers which are more powerful than classical computers, at least for certain problems. I shall focus on one approach to quantum computing, called the Quantum Adiabatic Algorithm, which is used to solve optimization problems, which are of great importance in science, engineering and industry. An optimization problem is one in which one has to minimize (or maximize) an energy function in which there is competition between different terms. I will discuss results both from computer modelling of the Quantum Adiabatic Algorithm and real experiments on a device which has of order 1,000 superconducting quantum bits. The difficulty of getting a "quantum speedup" from this device due to the great sensitivity of the ground state to changes in parameters (chaos) will be discussed.

The input-output relations of a biological system summarize its functional characteristics. Therefore, answering many fundamental questions on biomolecular machines ultimately reduces to understanding their input-output relations. Enzymes, that catalyze biochemical reactions, are among the simplest machines for which both input and output are chemical in nature. Many enzymatic reactions follow the "Michaelis-Menten" relations between input concentrations and output concentration of the molecular species involved in the reaction. We begin with a graph theoretic analysis of the input-output relation of a single enzyme. Input-output response of a graph can be characterized by the steady-state concentrations of the vertices. We present the conditions that must be satisfied by the structure of the graph (network) of states for the validity of the Michaelis-Menten input-output relation. This analysis sets the stage for understanding, at the next level of complexity, the input-output relation of a molecular machine, that is a macromolecular complex, and then at an even broader context of a group of interacting machines. I'll present an overview of our recent results on these input-output relations at multiple scales.

Reciprocity is a fundamental symmetry in physics; in optics it can be understood as the principle of ‘if I can see you, you can see me’. Breaking this symmetry results in asymmetric information transfer between two systems, i.e., the transmission amplitudes change under the exchange of source and detector. In the optimal situation, information transfer only occurs in one direction, which is a highly valuable feature for quantum information processing, where one aims to read out a quantum system while protecting the signal source. The violation of the symmetry of reciprocity requires rather special conditions, and one may ask the question if there is a general way to break reciprocity between two systems. This is indeed possible, we find that one can construct nonreciprocal interactions by combining the appropriate coherent and dissipative dynamics. Our nonreciprocity concept was experimentally confirmed within an optomechanical array setup in a collaboration with Oscar Painter’s group at Caltech. Furthermore, a number of related experiments can essentially be mapped to our approach as well. Overall, the nonreciprocity protocol is a powerful tool for realize directional interactions between two quantum systems and its full potential has yet to be explored. In this talk I give an introduction of the basic concept on how to engineer nonreciprocal interactions and devices.

Chiral spin liquids are highly entangled phases of interacting spins that break time reversal and inversion symmetries, but lack conventional magnetic order even at zero temperature. While chiral spin liquids have not been unambiguously observed in nature yet, they are expected to exhibit exotic properties following from a spectrum of fractional excitations. Theoretically, chiral spin liquids are often described by strongly coupled gauge theories which are hard to tackle analytically beyond mean-field approximations. In this talk, I will describe controllable approaches that allow us to understand various chiral spin liquids starting from lower-dimensional building blocks, namely arrays or junctions of Heisenberg spin chains. In the case of junctions, I will discuss the connection between chiral spin liquids and chiral fixed points of boundary conformal field theory.

The intimate connection between topology and quantum physics has been widely explored in solid-state physics, revealing a plethora of remarkable physical phenomena over the years. Building on their universal nature, topological properties are currently studied in an even broader context, ranging from ultracold atomic gases to photonics, where distinct observables and probes offer a novel view on topological quantum matter. In this talk, I will discuss how the geometry of quantum states can be revealed using a universal scheme based on excitation-rate measurements upon periodic driving [1,2,3]. When applied to Chern insulators or Landau levels, this approach leads to a quantized circular dichroism phenomenon [1,2], which can be interpreted as the dissipative counterpart of the quantum Hall effect. Besides, we will present protocols allowing for the experimental detection of the quantum metric tensor [3], which could be applied to detect new forms of monopoles in higher dimensions [4]. Finally, I will report on the first experimental observation of quantized circular dichroism in an ultracold Fermi gas [5]. [1] D. T. Tran, A. Dauphin, A. G. Grushin, P. Zoller and N. Goldman, Science Advances 3, e1701207 (2017). [2] D. T. Tran, N. R. Cooper, and N. Goldman, Phys. Rev. A 97, 061602(R) (2018). [3] T. Ozawa and N. Goldman, Phys. Rev. B 97, 201117(R) (2018). [4] G. Palumbo and N. Goldman, arXiv:1805.01247(2018). [5] L. Asteria, D. T. Tran, T. Ozawa, M. Tarnowski, B. S. Rem, N. Fläschner, K. Sengstock, N. Goldman and C. Weitenberg, arXiv:1805.11077 (2018).

Quantum communication allows us to solve tasks that are provably impossible using classical communication. A famous example is quantum key distribution which enables secure communication. Here, security can directly be traced back to fundamental properties of quantum entanglement, and is guaranteed even if an eavesdropper holds a quantum computer now or in the future. Many other applications have already been identified ranging from solving clock synchronization, to exotic applications such as extending the baseline of telescopes to make better observations. In this talk, we will give an overview of the state of the art of quantum communication, and look at how quantum entanglement might help us to solve cryptographic problems. We continue to look ahead to some of the many challenges to be solved in order to realize large scale quantum networks, which may eventually allow us to create entanglement between any two points on earth yielding new insights to physics, and bringing entirely new internet applications.

I will discuss recent developments in quantum simulation of quantum many-body systems with atomic platforms from a theory perspective. Systems of interests include atoms in optical lattices, Rydberg atoms in optical tweezer arrays, and trapped ions. Quantum simulation has so far been discussed as analog simulation, where we physically build a system with the desired Hamiltonian; or as digital quantum simulation, where time evolution of a many-body system is represented as a sequence of quantum gates on a quantum computer. I will add to this variation quantum simulation, where a quantum feedback loop between a classical computer and an analog quantum simulator, which acts as a quantum co-processor. As an example I will present results from an ongoing theory - experiment collaboration in Innsbruck: here our quantum resource is a trapped-ion 20-qubit analog quantum simulator, representing a transverse Ising model, and we compute on the quantum device the ground and excited states of the Lattice Schwinger Model as 1D Quantum Electrodynamics. Remarkably, variational quantum simulation allows "self-verification" of quantum results on the quantum machine, as assessment of the error. As a second topic we will discuss novel measurement protocols for Rényi entropies, and for out-of-time-ordered correlation functions (OTOCs), which can be extracted from on statistical correlations between randomized measurements. I will show a recent experiment with an ion chain, demonstrating experimental observation of entanglement entropies in quench dynamics in 10 and 20 qubit devices. I will conclude my talk with a brief outlook on possible future directions, including sub-wavelength optical lattices for atomic Hubbard models, and quantum chemistry.

The aim of this talk is two-fold. In the first part I want to explain how the study of interacting quantum gases in the continuum benefits from tools developed for quantum systems on the lattice, and how these tools appeared in the study of classical systems of the type of vertex models. These developments were carried out or were initiated by the many research activities of Prof. J. Zittartz especially in the late 80s and the 90s. In passing I want to point out how matrix-product and tensor-network states evolved in this environment and where the early exact and variational treatments led to. In the second part I will investigate the thermodynamics of the two-component one-dimensional Bose gas with contact interactions in the vicinity of the quantum critical point separating the vacuum and the ferromagnetic liquid regime. The quantum critical region is found to belong to the universality class of the spin-degenerate impenetrable particle gas which, surprisingly, is very different from the single-component case.

Fluids with an intrinsic gradient, for example in their temperature, charge, or density distribution, are known to produce a directed drift in suspended colloidal particles. This phenomenon is called phoresis. In this talk, I will summarize some recent theoretical work with the main focus on thermophoresis, mostly performed by means of mesoscopic simulations. These studies have also allow us to propose new applications in the design of promising phoretic machines such as microswimmers, turbines, or micropumps.

The theory of strong interactions, QuantumChromoDynamics, exhibits a strongly correlated low energy regime. This regime is governed by two phenomena, strong spontaneous chiral symmetry breaking and confinement. While the former phenomenon is responsible for most of the visible mass in the universe, the emergence of the latter is still not fully understood. Experimental access to QCD at large and small energies, temperatures and densities is obtained via heavy ion collisions within a non-equilibrium evolution. In summary the understanding of QCD requires theoretical approaches that can deal with both, strongly-correlated physics as well as non-equilibrium processes. The past years have seen tremendous progress in the description of QCD at vanishing and finite temperature and density with functional diagrammatic approaches, such as the functional renormalisation group or Dyson-Schwinger equations. Within these approaches QCD correlation functions of quarks, gluon and hadrons are computed non-perturbatively from first principles. In the present talk I will discuss respective results for strongly-correlated vaccum QCD, the phase structure of QCD at finite temperature and density, as well as its dynamics close to equilibrium. The talk concludes with a discussion of the further prospects for our understanding of the phase structure and dynamics of QCD.

Area laws were first discovered by Bekenstein and Hawking, who found that the entropy of a black hole grows proportional to its surface area, and not its volume. Entropy area laws have since become a fundamental part of modern physics, from the holographic principle in quantum gravity to ground state wavefunctions of quantum matter, where entanglement entropy is generically found to obey area law scaling. As no experiments are currently capable of directly probing the entanglement area law in naturally occurring many-body systems, evidence of its existence is based on studies of simplified theories. Using new exact microscopic path integral ground state Monte Carlo simulations of superfluid 4He, we demonstrate for the first time area law scaling of entanglement entropy in a real quantum liquid in three dimensions. We validate the fundamental principles underlying its physical origin, and present an "entanglement equation of state" showing how it depends on the density of the superfluid.

Why does the wave-function of a quantum system collapse during a measurement? It maybe possible to answer this question, as in the many-worlds interpretation, without modifying the theory. In this case, quantum theory is exact. On the other hand, it maybe that the theory has to be modified, as in the phenomenological model of Spontaneous Collapse. This model proposes that every quantum particle in nature undergoes spontaneous collapse, and that collapse is a fundamental property of nature, along with Schrödinger evolution. The predictions of this model differ from those of quantum theory, and we review the current experimental bounds on these models. We also review work which attempts to provide a theoretical underpinning for this phenomenological model, including the possible role of gravity, and a possible inter-connection between the measurement problem and the problem of time in quantum theory.

The quest for understanding and exploiting many-body phenomena has received new spur in the last decades by the increasing capacity of harnessing quantum particles to tailor more and more sophisticated systems. Among others, cold atomic gases are one of the most flexible platforms for realising such “Synthetic Quantum Matter”. Here, I focus on the interplay of geometrical constraints, tunable interactions of various range and (artificial) gauge fields to access i) interacting topological states of matter and ii) many-body effects in the transport properties of low-dimensional systems. In order to broaden our understanding, besides mappings onto effective models, I exploit quantum-information-inspired numerical techniques, namely Tensor Networks algorithms. In this way, insights about the entanglement structure of correlated states are also gained. In this talk, I will provide an overview of some of my recent results: in particular, I will concentrate on the Creutz-Hubbard ladder, a neat playground to address the above challenges, including the generation of flat bands as well as of non-doubled Dirac dispersion relations. In [1], I will present a theoretical analysis of the competition between correlated topological phases and orbital quantum magnetism, and the prediction of topological quantum phase transitions with different underlying conformal field theories (CFTs). In [2], I will examine the response of an interacting system of Dirac-Weyl fermions confined in a one-dimensional (1D) ring: i will show that the tuning of repulsive interactions leads to a unique many-body system that displays an enhancement of the Drude weight—the zero-frequency peak in the ac conductivity—with respect to the non-interacting value. Finally, I will review our proposal to experimentally realize this model in a synthetic ladder, made of two internal states of ultracold fermionic atoms in a one-dimensional optical lattice. References: [1] J. Jünemann, et al., PRX 7, 031057 (2017) [2] M. Bischoff, et al., PRB 96, 241112(R) (2017)

In standard formulations of the uncertainty principle, two fundamental features are typically cast as impossibility statements: two noncommuting observables cannot in general both be sharply defined (for the same state), nor can they be measured jointly. The pioneers of quantum mechanics were acutely aware and puzzled by this fact, and it motivated Heisenberg to seek a mitigation, which he formulated in his seminal paper of 1927. He provided intuitive arguments to show that the values of, say, the position and momentum of a particle can at least be unsharply defined, and they can be measured together provided some approximation errors are allowed. Only now, nine decades later, a working theory of approximate joint measurements is taking shape, leading to rigorous and experimentally testable formulations of associated error tradeoff relations. Here we briefly review this new development, explaining the concepts and steps taken in the construction of optimal joint approximations of pairs of incompatible observables. As a case study, we deduce measurement uncertainty relations for qubit observables using two distinct error measures. We provide an operational interpretation of the error bounds and discuss some of the first experimental tests of such relations. The talk is based on the review paper arXiv:1512.00104v3.

In recent years there have been important advances in understanding isolated quantum systems far from equilibrium. Prominent examples include the (pre-)heating process in the early universe after inflation, the initial stages in collisions of relativistic nuclei at giant laboratory facilities, as well as table-top experiments with ultracold quantum gases. Even though the typical energy scales of these systems vastly differ, they can show very similar dynamical properties. Certain characteristic numbers can even be quantitatively the same, defining nonthermal universality classes. One may use this universality to learn from experiments with cold atoms aspects about the dynamics during the early stages of our universe.

Starting from an amorphous partitioning of space into cells, we iteratively optimize the `centrality' of the cells, minimizing the so-called Quantizer energy. The energy landscape is replete with local minima to which the system converges despite the existence of lower-energy crystalline configurations. Irrespective of the level and type of disorder in the initial configurations, the tessellations converge to the same amorphous state, as measured by the same structure factor and energy distributions. The final disordered configurations exhibit an anomalous suppression of long-wavelength density fluctuations, known as hyperuniformity. For systems related to the Quantizer problem, such as selfassembled copolymeric phases, our findings suggest the possibility of stable disordered hyperuniform phases.

A question that attracted a lot of attention in the past two decades is whether biologically relevant search strategies can be identified by statistical data analysis and mathematical modeling. A famous paradigm in this field is the Levy Flight Foraging Hypothesis. It states that under certain mathematical conditions Levy dynamics, which defines a key concept in the theory of anomalous stochastic processes, leads to an optimal search strategy for foraging organisms. This hypothesis is discussed very controversially in the current literature. I will review examples and counterexamples of experimental data and their analyses confirming and refuting it. Related to this debate is own work about biophysical modeling of bumblebee flights under predation thread and biological cell migration, both based on experimental data analysis, which I briefly outline.

We study the contact process in the regime of small infection rates on scale-free networks evolving by stationary dynamics. A parameter allows us to interpolate between slow (static) and fast (mean-field) network dynamics. For two paradigmatic classes of networks we investigate transitions between phases of fast and slow extinction and in the latter case we analyse the density of infected vertices in the metastable state. This is joint work with Emmanuel Jacob (ENS Lyon) and Amitai Linker (Universidad de Chile).

One hundred and fifty years ago, Maxwell's demon was first posed as a fundamental challenge to the newly developed field of statistical physics. Just two months later, Maxwell's paper "On governors" gave the first analysis of a feedback system. These two foundational works reflect the fundamental and practical aspects of control. Here, I will present an experiment that unites the two: using feedback to create `impossible' dynamics, we make a Maxwell demon that can reach the fundamental limits to control set by thermodynamics. We test - and then extend - Rolf Landauer's 1961 prediction that information erasure requires at least as much work as can be extracted from a system by virtue of information. These fundamental thermodynamic limits are benchmarks for evaluating the performance of practical information engines, such as those active within cells and other complex systems.

Based on the recent conceptual and technical developments of quantum Monte Carlo simulations in correlated electron systems, I will present and discuss fresh results of itinerant quantum critical points, i.e., the critical phenomena arising from the strong coupling between Fermi surface and bosonic fluctuations, which are made possible by the self-learning Monte Carlo scheme. After which, I will also discuss the lately proposed duality relations between interaction-driven topological phase transitions and deconfined quantum critical points, which is verified via unbiased large-scale quantum Monte Carlo simulations.

Flows of large numbers of macroscopic particles (sand grains, cereals, ball bearings, etc.) occur in natural phenomena like land slides or avalanches and are an important part of many industrial processes. The flow behavior of granular fluids displays a rich rheology including Newtonian, shear thinning, and shear thickening regimes as well as the famous Bagnold scaling. The non-equilibrium nature of granular flows and the high densities and shear rates involved make a theoretical description challenging. I will begin with a qualitative discussion of what determines the flow behavior. Based on this discussion I will develop a theory from first principles that makes it quantitative and allows the prediction of flow curves and transport coefficients.

The previous 11 years have seen several breakthroughs in our understanding of topological states of matter. New Insulators and semimetals, exhibiting new properties imposed by a variety of symmetries (the most well known of which is time reversal) have been theoretically predicted and experimentally discovered. These materials are described by topological indices, a set of "serial numbers" that characterize the state of matter. In this talk, I will review the progress made in these years with a focus on the prediction of new topological indices and on material discovery. I will then show a surprising link between chemistry bonding and topological states of matter which leads to the prediction of many new classes of materials as topological.

We numerically explore the many body localization transition through the lens of the entanglement spectrum, i.e. the spectrum of the reduced density matrix. The level statistics of the entanglement spectrum as obtained through numerical diagonalization, unveil structures beyond that revealed by more limited measures such as entanglement entropy. We will also show that a simple artificial neural network trained on entanglement spectra of individual states of a many-body quantum system can be used to determine the transition between a many-body localized and a thermalizing regime.

The grand canonical ensemble lies at the core of quantum and classical  statistical mechanics. A small system thermalizes to this ensemble while exchanging heat and particles with a bath. A quantum system may exchange  quantities represented by operators that fail to commute. Whether such  a ​ ​ system thermalizes and what form the thermal state has are questions  about ​ ​ truly quantum thermodynamics. Here we investigate this thermal  state from ​ ​ three perspectives. First, we introduce an approximate microcanonical ensemble. If this ensemble characterizes the system- and-bath composite, tracing out the bath yields the system's thermal  state. This state is expected to be the equilibrium point, we argue,  of typical dynamics. Finally, we define a resource-theory model for thermodynamic exchanges of noncommuting observables. Complete passivity ​-- ​ the inability to extract work from equilibrium states ​ ​ -- ​, ​ implies  the thermal state's form, too. Our work opens new avenues into  equilibrium in the presence of quantum noncommutation. ​ [Based on arXiv:1512.01189]​

The prospect of intrinsically protected quantum computing is driving the research on topological quantum systems. Materials with a topologically nontrivial band structure are however difficult to manufacture experimentally. We recently showed that topological materials can be engineered by quite simple means, when considering a different space: superconducting junctions have the phase difference and the number of transported charges across the junction as conjugate variables. In the main part of the talk, I will present the example of a four-terminal junction whose energy spectrum exhibits Weyl singularities in the space of three independent phases, which thus play the role of quasimomenta. The nonzero Chern number can be directly probed through a transport measurement, namely, through a quantised transconductance. In the final part of the talk, I will provide an outlook on future directions. For one, electric circuits may be used to study topological phase transitions specific to open systems out of equilibrium, and secondly, they may exhibit a so far unexplored connection between topology and quantum thermodynamics.

The analysis of topological excitations in interacting many-body systems often provides important insights into quantum phases and phase transitions. Seminal examples are the (thermal) BKT transition as well as the (quantum) superfluid-Mott insulator transition, which are naturally described in terms of vortices. More recently, such a ‘dual’ formulation has proven extremely illuminating in the study of exotic phases of matter that host fractional excitations, e.g., in topological phases and quantum magnets. In my talk, I will review the dual description of conventional phases of matter and explain how exotic, fractionalized phases are captured within this approach. I will then generalize these dualities to fermionic systems, and discuss the implications for the half-filled Landau level and strongly interacting surfaces of topological insulators. Finally, I will describe how two-dimensional Dirac fermions (and their symmetries) can be mapped onto interacting bosons.

The control of quantum states is essential both for fundamental investigations and for technological applications of quantum physics. In quantum few-body systems, decoherence arising from interaction with the environment hinders the realization of desired processes. In quantum many-body systems, complexity of their dynamics further makes state preparation via external manipulation highly non-trivial. An effective strategy to counter these effects is offered by quantum optimal control theory, exploiting quantum coherence to dynamically reach a desired goal with high accuracy even under limitations on resources such as time, bandwidth, and precision. In this talk I will (i) introduce the quantum optimal control method we developed to this aim, the CRAB (Chopped Random Basis) algorithm, (ii) present experimental results obtained via its application to various physical systems, from quantum logical operations in solid-state quantum optics to quantum criticality in ultra-cold atoms, (iii) use these examples to illustrate the quantum speed limit, i.e. the maximum speed achievable for a given quantum transformation, and (iv) propose a way to characterise the latter in an information-theoretical fashion by the bandwidth of the optimized control pulses.

The laws of thermodynamics can be extended to mesoscopic systems for which energy changes are on the order of the thermal energy are relevant. Therefore, thermodynamic observables associated with mesoscopic degrees of freedom are stochastic. A key example of such thermodynamic observable is the stochastic entropy production in nonequilibrium processes. Little is known beyond fluctuation theorems about universal statistics of entropy-production fluctuations. Using Martingale theory we have discovered novel universal statistics of stochastic entropy production in nonequilibrium steady states such as: (i) The distribution of the negative record (which we call infimum) of entropy production (ii) the passage probabilities of entropy production; (iii) the stopping-time fluctuations of entropy production. Our work is based on the finding that in a nonequilibrium steady state, the exponential of minus the entropy production is a martingale process. A martingale is a process representing a fair game with no net gain or loss and its connection to thermodynamics has not been fully explored yet. Notably, our results have interesting implications for stochastic processes that can be discussed in colloidal systems and active molecular processes. For example, we make predictions for the distribution of the maximum backtrack depth of RNA polymerases during transcription.

We consider a one-dimensional model that describes the depinning of an elastic chain of particles in a strongly pinning, phase-disordered periodic environment under a slowly increasing driving force. The evolution towards depinning occurs by the triggering of avalanches in regions of activity which are at first isolated, but later grow and merge. For large system sizes the dynamically critical behavior is dominated by the coagulation of these active regions. Our analysis and numerical simulations show that the evolution of the sizes of active regions is well described by a Smoluchowski coagulation equation, allowing us to predict correlation lengths and avalanche sizes in terms of certain moments of the size distribution. Time permitting, we will also briefly present work in progress on the thermal behaviour of the model.

Extremely floppy molecules are indescribable by the common ideas of molecular physics. Their ground state wave functions are highly delocalized and the concept of molecular structure breaks down. Recently, we established a fundamentally new 'super-rotor' model, which is based on a five-dimensional rotational symmetry. The respective states are described by the irreducible representations of SO(5) and the Hamiltonian is proportional to the respective Casimir operator. The prototypical example of floppy molecules is protonated methane, which was measured only recently in the Cologne lab. With our simple model, we are - for the first time - able to predict energy levels which actually compare very favourably to the experimental values. In addition, the exchange symmetry of the protons can be determined by using an isomorphism of the permutation group to a subgroup of SO(5). In this talk, we discuss the basic concepts of this new approach and ask some of the most urgent questions for further developments.

The elastic properties of materials are determined by a few material constants such as the Young’s modulus. Using super-structures one can effectively change these “constants”. In this way we obtain functionalities such as wave-guiding, acoustic lensing or programmable failure. I will show how topological band theory, known from the description of electrons in solids, provides us with a powerful design-principle for such mechanical metamaterials.

Concepts based on multi-particle interference have been proven very fruitful for better understanding various different many-body phenomena, including quantum dynamics of cold atoms, "many-body localization", correlated transport through molecules, or scattering in photonic networks. We will consider such phenomena using semiclassical techniques based on interfering Feynman paths. A major objective of such approaches to an interacting many-body system is to combine information of its two complementary classical limits, namely a classical system of particles and/or a classical field theory, into a unified framework, providing a picture of many-body interference based on coherent sums over classical solutions. Following this direction we will illustrate recent progress in the semiclassical analysis of many-body interference using a prime example of integrable quantum field theory, the Lieb-Liniger model, describing interacting bosons on a ring. We show that, in the limit of high excitations, its spectrum can be understood by means of suitable generalizations of the so-called Weyl expansion for the smooth part, and a trace formula for the oscillatory part, revealing a spectral shell structure in terms of many-body periodic orbits. We will then show how for large particle number the complementary classical limit of the Lieb-Liniger model, given by a nonlinear Schroedinger equation, admits as well an analysis as an integrable classical system, now near its ground state. This enables the description of a sequence of quantum phase transitions arising for increasing (attractive) interaction, along with an understanding of numerical results for the spreading of information around criticallity. In the opposite case of non-integrable systems, applications of many particle interference comprise coherent backscattering and echo phenomena in Fock space.

Hawking's prediction that black holes should radiate was one of the biggest surprizes in physics of the late 20th century. It has dominated much of the study in the interface between gravity and Quantum Mechanics ever since. The calculation Hawking presented is problematic, and thus experimental confirmation would be good. Unfortunately, finding small black holes is hard. However, there turn out to be analog systems, systems with horizons which one can and is studying in the lab. I will present the arguments and the current experimental effort to see the radiation, and the arguments that some experiments have already seen it.

Interface growth is a paradigmatic example of a complex system made from a large number of strongly interacting degrees of freedom, with dynamically created long-range correlations. Such systems can undergo physical ageing, that is they display (i) slow relaxational behaviour, (ii) breaking of time-translation-invariance and (iii) dynamical scaling. Through simulations and simple exactly solvable models, we investigate into the existence of new, non-trivial dynamical symmetries extending dynamical scaling and their possible consequences.

The inverse Ising problem seeks to reconstruct the parameters of an Ising Hamiltonian on the basis of spin configurations sampled from the Boltzmann measure. The last decade has witnessed many applications of the inverse Ising problem driven by the advent of large-scale data in different scientific disciplines, especially biology. In this talk I will give an introduction to the inverse Ising problem, discussing its applications as well as different approaches from statistical physics. A particular focus is on the link between approaches to the inverse Ising problem based on the optimisation of some `objective function' and the statistical physics of disordered systems. This allows to characterise the performance of an arbitrary objective function and to calculate the objective function which optimally reconstructs the model parameters.

The last years have witnessed dramatic progress in experimental control and theoretical modeling of quantum simulations based on ultracold atoms. Major recent developments include synthetic gauge fields for neutral atoms, which allow the simulation of topologically nontrivial phases of matter with strong interactions. I will discuss two examples:  We consider a spinful and time-reversal invariant version of the Hofstadter-Harper problem, which has been realized in ultracold atoms, with an additional staggered potential and spin-orbit coupling. Without interactions, the system exhibits various phases such as topological and normal insulator, metal and semi-metal phases with two or even more Dirac cones. Using real-space dynamical mean-field theory (DMFT), we investigate the stability of the Quantum Spin Hall state in the presence of strong interactions. To test the bulk-boundary correspondence between edge mode parity and bulk Chern index of the interacting system, we calculate an effective topological Hamiltonian based on the local self-energy of DMFT.  We furthermore investigate the Haldane honeycomb lattice tight-binding model, for bosons with additional local Hubbard interactions. We analyze the ground state phase diagram at filling one, and uncover three distinct phases: a uniform superfluid (SF), a chiral superfluid (CSF) and a plaquette Mott insulator with local current loops (PMI). 

Cells have the ability to generate mechanical forces. Coordination of these forces is not only important for multicellular life, but also plays a role for various diseases. We combine physical theory and traction microscopy to uncover mechanisms of how cells feel and respond to forces. Here, we present a synopsis of recent findings on mechanisms of collective organization, ranging from bacteria to eukaryotic tissue cells.

I will present recent progress on Majorana fermions and other exotic excitations with non-Abelian braid statistics that can emerge in condensed matter systems. These excitations have attracted wide attention recently, also because of their potential applications in topological quantum computing. Majorana fermion zero-modes and their generalizations, parafermions, can emerge in nanowires and atomic chains in the presence of spin orbit interaction or spatially periodic magnetic fields, in RKKY systems forming intrinsic spin helices, in topological insulators, and typically in the presence of superconductivity. I will discuss some candidate materials such as semiconducting Rashba nanowires and atomic magnetic chains and show some recent experimental progress. Finally, I plan to discuss parafermions, which, in contrast to Majorana fermions, can emerge only in the presence of strong electron-electron interactions and have a more powerful braid statistics that enables entanglement and in particular exact CNOT gates by braiding alone (without the need of any measurements).

The dynamics of interacting Brownian particles can be described by a stochastic  equation for the density field. I will show how the linearised version of this  equation can be used to recover, very simply, certain of Onsager's results  on electrolyte conductivity. In addition I will show how it can analyse the  out of equilibrium thermal Casimir effect between parallel plates containing  Brownian charges, in particular the case where the plates are held at different temperatures and when an electric field drives a current in one of the plates.

The recent discovery of the Higgs boson at the LHC marked the completion of the theoretical description of strong, weak and electromagnetic interactions among the known elementary particles and builds up the basis of the Standard Model (SM) of particle physics. This talk will provide an introduction into the physics of Higgs bosons and their quantitative tests at the LHC. This includes the decay and production profile of the SM Higgs boson and will also make remarks about extensions of the SM and their Higgs bosons.

Since their discovery in 1971 the superfluid phases of Helium-3 have proved to be the ideal testing ground for many fundamental concepts of modern physics. Phenomena such as anisotropic Cooper pairing, p-wave states, chirality, macroscopic quantum coherence, spontaneous breaking of high symmetries, and exotic topological defects are not only an important enrichment of the physics of condensed matter, but also provide important links to particle physics, defect formation in the early universe and, most recently, quantum turbulence. I will present an introduction into the physics of superfluid Helium-3 and describe the progress made in this fascinating field of basic research.

The Kardar-Parisi-Zhang (KPZ) equation describes an important universality class of nonequilibrium stochastic models, including stochastic interface growth. There has been much recent interest in the one-point probability distribution P(H, t) of height H of the evolving interface at time t. I will show how one can use the weak-noise theory (also known as the optimal fluctuation method, the macroscopic fluctuation theory, or simply WKB) to evaluate P(H, t) for different initial conditions. At small t and H, P(H,t) is Gaussian, but its tails are non-Gaussian and highly asymmetric. In a proper moving frame, one of the tails agrees at all times with the asymptotics of the Tracy-Widom distribution (for the flat and curved interface), and of the Baik-Rains distribution (for the stationary interface), previously observed at long times. The other tail displays a behavior that differs from the known long-time asymptotics. We argue that this tail should be also observable at long times once |H| is very large. The case of stationary interface is especially interesting. Here at short times the large deviation function of the height exhibits a singularity at a critical value of |H|.

According to the no-hair theorem, the Kerr-Newman black hole solution represents the most general asymptotically flat, stationary (electro-) vacuum black hole solution in general relativity. The talk shows how this solution can indeed be constructed as the unique solution to the corresponding boundary value problem of the axially symmetric Einstein-Maxwell equations in a straightforward manner.

The textbook uncertainty relation due to Kennard, Weyl and Robertson is a "preparation uncertainty relation", which constrains how sharply the position and momentum distributions of a fixed state can be concentrated. It has nothing to say about error -disturbance tradeoffs for setups like Heisenberg's gamma-ray microscope from 1927. Formulated by Heisenberg only as a heuristic principle, this tradeoff links the accuracy of an approximate position measurement to the possibility to retrieve the momentum after the measurement. We generalize this problem to a simpler one, namely the quality of optimal joint measurements of position and momentum. It is then only required that a device provides a position value and a momentum value in each shot, like the microscope and the momentum retrieval in the error/disturbance case. We will show quantitatively that the distribution of the position outputs must in general differ from that of an ideal position measurement, and similarly for momentum, where the respective deviations satisfy a relation looking formally like the textbook preparation uncertainty relation. Our setup is conceptually straightforward and covers arbitrary pairs or tuples of observables. It turns out that the equality of the preparation and measurement uncertainty bounds is due to the high symmetry of canonical pairs of observables linked via Fourier transform. For generic pairs of observables the measurement uncertainty is larger than the preparation uncertainty.

Microbial laboratory communities have become model systems for studying the complex interplay between nonlinear dynamics of evolutionary selection forces, stochastic fluctuations arising from the probabilistic nature of interactions, and spatial organization. Major research goals are to identify and understand mechanisms that ensures viability of microbial colonies by allowing for species diversity, cooperative behavior and other kinds of social behavior. A synthesis of evolutionary game theory, nonlinear dynamics, and the theory of stochastic processes provides the conceptual framework for a deeper understanding of these ecological systems. In this talk, we will give an introduction into the modern formulation of these theories and illustrate their effectiveness focusing on selected examples of microbial systems. We also discuss current challenges and future perspectives in quantifying bacterial population dynamics, and how this might have an impact on research in non-equilibrium physics.

We use the universal nonlinear fluctuating hydrodynamics approach to study anomalous one-dimensional transport far from thermal equilibrium in terms of the dynamical structure function. Generically for more than one conservation law mode coupling theory is shown to predict a discrete family of dynamical universality classes with dynamical exponents which are consecutive ratios of neighboring Fibonacci numbers, starting with z = 2 (corresponding to a diffusive mode) or z = 3/2 (Kardar-Parisi-Zhang (KPZ) mode). If neither a diffusive nor a KPZ mode are present, all Fibonacci modes have as dynamical exponent the golden mean z=(1+\sqrt5)/2. The scaling functions of the Fibonacci modes are asymmetric Levy distributions which are completely fixed by the macroscopic stationary properties, viz. the current-density relation and the compressibility matrix of the system. The theoretical predictions are confirmed by Monte-Carlo simulations of a three-lane asymmetric simple exclusion process.

The field of thermodynamics is one of the crown jewels of classical physics. Extending its ideas and concepts to the non-equilibrium setting is a challenging topic of perennial interest. Here, we study perhaps the simplest non-equilibrium class of quantum problems, namely Floquet systems, i.e. systems whose Hamiltonians depend on time periodically, H(t+T) = H(t). For these, there is no energy conservation, and hence not even a natural definition of temperature. We find that it is nonetheless possible to identify three fundamentally distinct thermodynamic ensembles. We also ask if there exists a sharp notion of a phase in such driven, interacting quantum systems. Disorder turns out to play a crucial role, enabling the existence of states which are straightforward analogues of equilibrium states with broken symmetries and topological order, while others - genuinely new to the Floquet problem - are characterized by a combination of order and non-trivial periodic dynamics.

Classification of quantum phases is one of the central problems in statistical mechanics and condensed matter physics. Traditionally, it had been associated to spontaneous symmetry breakings. However, a rich variety of quantum phases without any spontaneous symmetry breaking have been found and dubbed as topological phases. Symmetries can still play an important role even when there is no spontaneous symmetry breaking, as some quantum phases are distinct only in the presence of certain symmetries. I will review the concept of "symmetry-protected topological phases" and then discuss our recent attempts in generalizing the notion of symmetry protection of quantum phases.

Stochastic thermodynamics offers a powerful formalism to study fluctuating thermodynamic variables, such as (free) energy, entropy, heat, and work in small systems driven beyond the linear response regime. Small electronic devices, such as single-electron boxes and quantum dots have been recently shown to provide well-controlled benchmarks for stochastic thermodynamics. In particular, it is possible to realize the ubiquitous concepts of a Szilard engine and a Maxwell’s demon in such systems. While stochastic thermodynamics gives a complete theoretical picture for devices such as the Maxwell’s demon at classical level, attempts to generalize the concept of work (and other thermodynamic quantities) to open quantum systems have met with some difficulties. The main problem in quantum mechanics is that there is no unique work operator, since for irreversible processes work depends both on the state of the system as well as the path taken. In this talk I will discuss the analysis of devices such as the Maxwell’s demon based on stochastic thermodynamics at the classical level. I will then describe some recent progress in defining work and its moments for quantum systems within the two-measurement protocol (TMP) approach, which for isolated systems coincides with the classical definition of work in the appropriate limit. In particular, I will show that using the TMP within the Linblad master equation formalism yields explicit results for driven, open quantum systems.

Absent words are sub-sequences of letters that cannot be found in a given text. Minimal absent words (MAWs) are absent words all of the sub-sequences of which can be found in the text. It has been observed for some time that the length distribution of MAWs in genome sequences have a curious two-mode structure with on the one hand many long fairly short MAWs ("the bulk") and on the other hand some very long MAWs ("the tail"). I will show that the first feature arises from statistical sampling of sub-sequences from a random genome while the second can be explained by a simple probabilistic model of genome evolution. Tail MAWs also seem to carry biological information as will be discussed in the talk. We were led to the study of MAWs from a biotechnological problem of optimal tag design for (tagged) RNA-sequencing. I will therefore also describe some of the results obtained by this method to distinguish primary from processed RNA in the human pathogen Enterococcus faecalis, including the discovery of many new non-coding genes in this organism.

The talk is divided into two parts. In part one, we discuss universal aspects of quantum dynamics present in driven open many-particle systems. Oftentimes, driven systems show full decoherence at large wavelength, but we present two situations which do not follow this generic pattern. The first concerns the critical dynamics in a driven open system with a dark state realizable in microcavity arrays, and the other one an ensemble of Rydberg atoms, in which coherent quantum dynamics leads to a variant of a non-equilibrium absorbing state transition without direct classical counterpart. In part two, we discuss, in a number conserving framework, an exactly solvable model of interacting fermions supporting non-local zero-energy Majorana-like edge excitations. The construction draws intuition from an approach of targeted dissipative cooling into topologically non-trivial states. The model has an exactly solvable line, on varying the density of fermions, described by a topologically non-trivial ground state wave-function. We characterize its thermodynamic and topological properties. Knowledge of the ground state wavefunction allows us to construct analytically number conserving braiding operators, which are exponentially localized at the edges.

Every time the release button of a digital camera is pressed, several megabytes of raw data are recorded. But the size of a typical jpeg output file is only 10% of that. What a waste! Can't we design a process which records only the relevant 10% of the data to begin with? I will give an introduction to the concepts and math of compressed sensing - a theory that achieves this trick for certain signals. A variant of compressed sensing aims to exploit representations of data in terms of low-rank matrices. There has been a fruitful exchange of ideas between this theory and quantum physics. Methods that we had originally introduced in the context of quantum state estimation have since found applications to tasks as diverse as face recognition, the analysis of x-ray diffraction images, and the prediction of user preferences in online shops. Specific quantum information ideas that feature in this context including trace inequalities and their use to prove large deviation bounds for random matrices, phase space methods, and the notion of complex projective designs.

A moving interface, or a front, between a stable and an unstable medium is often described by an equation such as the Fisher-KPP (Kolmogorov-Petrovsky-Piscounov) equation. Such an equation appears in biology, chemistry or theoretical physics. Thirty years ago, Bramson gave rigorous sharp estimates on the position of the front, and, fifteen years ago, Ebert and van Saarloos heuristically identified universal vanishing corrections. In this seminar, I will present two new front equations which we believe to be in the same universality class as the Fisher-KPP equation. For the first equation, we can write an exact relation between the initial condition and the positions of the front at all times. For the second equation, probabilistic methods give very good estimates on the shape of the front at all times. In both cases, we can recover and make precise the universal vanishing corrections on the position of the front.

The Pauli exclusion principle is a constraint on the natural occupation numbers of fermionic states. It has been suspected for decades, and only proved very recently, that there is a multitude of further constraints on these numbers, generalizing the Pauli principle. Surprisingly, these constraints are linear: they cut out a geometric object known as a polytope. This is a beautiful mathematical result, but are there systems whose physics is governed by these constraints? In order to address this question, we studied a system of a few fermions connected by springs. As we varied the spring constant, the occupation numbers moved within the polytope. The path they traced hugs very close to the boundary of the polytope, suggesting that the generalized constraints affect the system. I will mention the implications of these findings for the structure of few-fermion ground states and then discuss the relation between the geometry of the polytope and different types of fermionic entanglement.

Cells can measure chemical concentrations with extraordinary precision. This raises the question what is the fundamental limit to the accuracy of chemical concentration measurements. In this talk, I will show that the sensing accuracy of passive signaling systems is limited by the number of receptors; a downstream processing network can never increase the sensing precision beyond this limit. Non-equilibrium systems can beat this limit. However, this requires receptors and their integration time, downstream molecules, and energy. Each resource imposes a fundamental sensing limit, which means that the sensing precision is bounded by the limiting resource and cannot be enhanced by increasing another resource. This result yields a new design principle, namely that of optimal resource allocation in cellular sensing. It states that in an optimally designed sensing system, each resource is equally limiting, so that no resource is wasted. We find that the chemotaxis network of E. coli obeys this principle, indicating a selective pressure for the efficient design of cellular sensing systems.

One-dimensional branching Brownian motion has been the subject of intensive research, in particular during the last decade. We consider the discrete space version of branching random walk and investigate the setting of a spatially random branching environment; in particular we are interested in the position of the maximal particle. Via the Feynman-Kac formula this is connected to fluctuations of the solutions to the parabolic Anderson model (i.e., the heat equation with a random potential) as well as to a randomized version of the Fisher-KPP equation. The Fisher-KPP equation is a fundamental reaction-diffusion partial differential equation which had originally been introduced in order to model the spread of an advantageous alelle in a population of a one-dimensional habitat.

Swimming of Bacteria at low Reynolds numbers is relatively well understood. Much less is known about bacteria crawling on surfaces. In particular as some species leave sticky trails that are believed to help them coordinate. I will introduce a simple semi-microscopic model for the bacteria-trail interaction. Based on this model I will discuss the effects of the trail-mediated self-interaction on a single bacterium and whether or not it actually allows trail-following behaviour.

It is a relatively new insight of classical statistics that empirical data can contain information about causation rather than mere correlation. Within that context, during the past year we have developed and formalized a new research program for the study of causal relations in both the classical and quantum cases. In this presentation we will discuss two recent developments that highlight the very fruitful interplay between the causal inference literature and problems in quantum information, a connection which is increasingly appreciated among quantum physicists. We will describe a general algorithm for computing information-theoretic constraints on the correlations that can arise from a given causal structure, where we allow for quantum systems as well as classical random variables. In a second part, we will revisit nonlocality from a causal inference perspective and give an answer to the following question: How much do we need to relax the causal assumptions entering in Bell's theorem to classically explain nonlocal correlations?

Modern physics describes matter and their interactions on the fundamental level as quantum fields. Already their ground state - the quantum vacuum - exhibits properties analogous to complex media: fluctuations of quantum fields can induce nonlocal and nonlinear phenomena. This talk gives an overview on present experiments using strong fields for probing the quantum vacuum. Illustrative theory methods will be discussed that help to understand quantum fluctuations and quantum vacua intuitively. Recent ideas will be highlighted that aim at searches for "New Physics" with strong fields.

It is explained how, in quantum mechanics, information about a physical system is acquired through direct (von Neumann) and indirect (Kraus) measurements/observations. In a first part, a new theory of direct (projective, or von Neumann) measurements is developed, using methods and results from functional analysis. In a second part, the theory of indirect measurements is sketched, and it is shown how various theorems from probability theory and statistics can be used for this purpose. Many of the general ideas are explained in the context of a simple model system. Time permitting, I will outline tentative applications of the main ideas presented in this talk to a theory of perception.

Famously, Anderson showed in 1958 that non-interacting quantum mechanical electrons placed in a random potential could fail to exhibit diffusion. In 2005 Basko, Aleiner and Altshuler put the long conjectured extension of the Anderson localization to the interacting setting, termed Many Body Localization, on a much firmer footing setting off a rapidly growing volume of work on this phenomenon. I will describe the broad outlines of this work and discuss how it has both enriched our understanding of the foundation of quantum statistical mechanics and led to the remarkable notion of non-equilibrium quantum phase structure that lies outside the former.

We will discuss the intimate connection existing between information theory and thermodynamics following its historical development. We will focus on two complementary aspects: 1) the gain of information which we will illustrate with Maxwell's famous demon and 2) the erasure of information summarized by Landauer's principle. We will further present a number of recent single-particle experiments that have for the first time realized the above gedanken experiments in the lab.

Coupled-dimer magnets have become model systems in the study of quantum phase transitions. After a brief introduction to quantum criticality in magnets, the talk will discuss various theoretical approaches to describe coupled-dimer magnets, using both field-theoretic and microscopic techniques, and link the results to experimental observations. In particular, a novel expansion in 1/d will be presented where d is spatial dimensionality. In addition, interesting phenomena arising from quenched disorder in coupled-dimer magnets will be highlighted, both for dilute and dense concentration of defects.

The anisotropic Heisenberg chain of spins 1/2 is one of the key paradigms of strongly correlated electrons in one dimension. While equilibrium properties of the model are relatively well understood, even very basic questions about its non-equilibrium properties were still open until very recently. A prominent example is the question whether the model exhibits ballistic spin transport at finite temperatures or not? I will outline the progress on this topic which has been triggered by the discovery of exact solution of quantum master equation of the boundary driven Heisenberg chain. The steady-state solution of non-equilibrium master equation leads to novel quasi-local conservation laws, which in turn lead to a derivation of rigorous strict lower bounds on ballistic transport coefficients. I will also explain how such an approach of `non-equilibrium integrability' works for some other strongly interacting quantum chains, for instance, for the Hubbard model or Lai- Sutherland model of spins 1.

In this talk I will discuss how entanglement and the eigenstates (natural orbitals) and eigenvalues (occupations) of the one-particle density matrix can be used to characterize the many-body localization transition and phases. Many-body localization is the interacting version of the Anderson insulator, and is reflected both as localization of particles in real space, as well as in Fock-space. The study of entanglement, both in eigenstates and its evolution after quenches, has been instrumental in advancing our understanding of many-body localized phases. The entanglement entropy of eigenstates goes from an area law in the localized phase, reflecting the real space localization of wave functions, to an volume law in the delocalized phase, with diverging fluctuations at the transition. In contrast, a global quench within the many-body localized phase gives rise to a slowly (logarithmically) increasing entanglement entropy. The entropy of occupations in the one-particle density matrix turns out to have similar properties as the entanglement entropy--area law in localized phase, volume law in delocalized phase, and diverging fluctuations at the transition--but this is reflecting the Fock space structure of the eigenstates. Finally, the inverse participation ratio of the natural orbitals can be used to define a one-particle localization length in the localized phase.

Starting with Maxwell's equations for the electromagnetic field (1865), we first point out how Maxwell brought his system of equations into quaternionic form. Subsequently, we recognize that what we call Maxwell's equations nowadays is a creation of Heaviside and Hertz. Then we study the impact of special and of general relativity on Maxwell's equations. In particular we follow up the metric-free and topological version of Maxwell's equations via exterior differential forms and period integrals and discuss some applications. Alternative formulations via spinors, Clifford algebras, chains and cochains... are shortly mentioned.

Growth of solid tumors or metastasis requiers, besides massive biomedical changes, also a spatial remodeling of the tissue. This remodeling, often including displacements of healthy tissue around, requires mechanical work to be done. These mechanics of growth has attracted a lot of attention in recent years, but still remains poorly understood. We use particle based simulations to study mechanical properties and effects in growing and motile tissues. These simulations have been helpful in understanding, interpreting and designing experiments. I will present an overview of the simulation thechnique, and how it contributed to recent develobments in three dimensional tissue growth and collective cell migration. In a recent series of simulations and close experimental collaborations we found important interfacial and surface effects that lead to novel phenomena. For example, the tissue divides favorably at a free surface, even without any nutrient effects. This leads to the possibility and stability of a negative homeostatic pressure. In turn, a negative homeostatic pressure leads to naturally to finite steady states and tensile states.

Blood flow plays an important role in many physiological processes and pathologies in the organism. To understand these processes, detailed investigation of blood flow is required under realistic conditions including cell deformability, hydrodynamic interactions, and complex geometries. We employ the smoothed dissipative particle dynamics method, a mesoscopic hydrodynamic simulation technique, to model blood as a suspension of deformable cells represented by a viscoelastic spring-network which incorporates appropriate mechanical and rheological cell-membrane properties. Blood flow in idealized micro-channel geometries will be investigated. We will discuss the physical mechanisms which govern migration of micro- and nano-carriers toward the walls in micro-vessels. Moreover, we will present the flow behavior of blood cells in a microfluidic device which offers great opportunities for cell sorting. We will illustrate the use of complex flow geometries to separate cells of different sizes and the application of realistic blood flow simulations to optimize the device performance.

In this talk, various universality classes found in absorbing phase transitions will be reviewed. Starting from the contact process, the directed percolation (DP) universality class and a possible classification scheme known as the DP conjecture will be discussed. The DP conjecture states that a model system without nontrivial symmetry and/or conservation laws and with a single order parameter field should belong to the DP class. Other universality classes have been found by breaking some of the requisites of the DP conjecture, which will be briefly discussed. Particular focus of this talk will be on a controversy around the universality class to which the pair contact process with diffusion (PCPD) should belong. Two conflicting viewpoints and their supporting arguments will be reviewed. Endeavors to settle down this controversy will be discussed.

Recent experiments on the dynamics of ultra-cold atomic gases have opened up completely new ways to study far-from-equilibrium quantum states. These intriguing prospects triggered tremendous experimental and theoretical developments and have led to an extremely active research field. In particular, strongly correlated quantum systems have been at the forefront of theoretical research since they show non-trivial many-body effects. I will give a brief overview over these developments with an emphasis on the dynamics of one-dimensional systems, where the dynamics may be restricted by the existence of non-trivial integrals of motion linking it to the field of integrable systems. I will then present results on the universality of the time evolution in both massive and massless systems and discuss the effects of finite quench times.

Quantum optical realizations of many-body systems must often be considered as open systems and thus offer a way to study quantum correlations and phase transitions in a non-equilibrium steady-state. The competition between interactions and fluctuations inherent to an open system will be discussed for the experimentally relevant examples of optically driven Rydberg gases and Rydberg polaritons. The steady-state phase transition to crystalline order in a lattice gases will be discussed as well as the dynamics of its build-up. In the second part photons coupled to Rydberg atoms under conditions of electromagnetically induced transparency will be considered. The coupling results in strongly interacting polaritons, which behave like hard-sphere objects with non-local interaction giving rise to a non-local nonlinear optics.

We deduce the generic phase diagrams encoding the distinct localized and delocalized phases of noninteracting fermionic quasiparticle for any symmetry class from the tenfold way in one, two, and three dimensions. To this end, we start from a massive Dirac Hamiltonian perturbed by a generic disorder for any dimension of space and for any one of the ten symmetry classes from the tenfold way. The physics of Anderson localization is then encoded by a two-dimensional phase diagram that we deduce from the topology of the space of normalized Dirac masses.

Recently interest of discontinuous percolation transitions (DPT) has been boosted in complex systems, because the DPT can be found in many real-world systems such as epidemic spreading and cascading failures of inter-dependent infra-structure. Nevertheless, many fundamental questions remained unsolved yet. One of them was to invent the model exhibiting the DPT in cluster merging processes and to understand diverse properties arising in such models. In my talk, I will present recent theoretical research progress of the DPT in the cluster merging processes, which includes models, properties of DPTs, and future works.

Recent experimental developments in quantum optics have opened up possibilities to create strongly correlated states of matter with sizable electromagnetic or photonic components. Enabled by strong atom-photon coupling on the single-quantum level, for example in cavity QED and with Rydberg atoms, it is now possible to study the statistical, and generically far-from-equilibrium, physics of photons in new regimes far beyond what is know from the laser theory developed in the 1970's. Here, I will survey our first attempts to classify such phases of photonic matter into universality classes including glasses, superradiant Fermi gases, and attractive quantum liquids. In the second part, I will consider electronic materials in which frustration and interactions are so strong that, collective excitations made out of electronic spins behave as emergent photons, and compute new observable signatures thereof. Further information: http://www.thp.uni-koeln.de/~strack/

I will give an overview of recent work on the physics of lattice models of close-packed loops. The models have two phases -- one in which all loops are finite, and another in which some loops are extended -- and the interest is in universal features of these phases and the transitions between them. The models describe a number of problems in classical statistical physics -- where, for example, the loops may be vortex lines in a three-dimensional random field -- and also many-body quantum systems -- where the loops are world-lines of particles.

Modern theories of cosmology assume that the Universe underwent a period of exponential expansion ("inflation") at an early stage. Inflation does not only solve some of the conceptual problems of earlier cosmological models, but also allows a causal explanation of structure formation. Moreover, it necessarily predicts the creation of gravitons, the spin-2 particles associated with the quantized gravitational field. In March 2014, the south-pole experiment Bicep2 announced the observational confirmation of such primordial gravitons. If true, this would constitute a major step towards an understanding of quantum gravity and the origin of our Universe. In my talk, I shall summarize the physics that is needed to understand this result, review the observations, and give an outlook on future developments.

To efficiently catalyze multi-step biochemical reaction pathways, cells have optimized the synergistic action of a multitude of enzymes. They not only control the concentrations and activities of enzymes, but often also coordinate enzymes from the same biochemical reaction pathway by arranging them in self-assembled multi-enzyme complexes. Such complexes are the basis of `channeling' mechanisms, where intermediate products in multi-step reactions are effectively passed from one enzyme to the next. These same principles can be applied in artificial nano-scale systems, with the ultimate goal to control and optimize biochemical reactions at will, e.g. for the production of medical substances or renewable energy sources. While enzymatic activity has been studied for over a century, quantitative experiments were limited to the bulk level until the recent advent of single-molecule enzymology techniques, which permit the quantitative characterization of the stochastic reaction dynamics of enzymes. Single-molecule experiments with enzymes have also spurred the theoretical analysis of stochastic enzyme dynamics, but the theoretical description and analysis of enzyme complexes is only beginning to develop. I will describe some recent progress in this direction.

One of the most intriguing phenomena in strongly correlated systems is the fractionalization of quantum numbers - familiar examples include the spin-charge separation in one-dimensional metallic systems, the fractionalization of the electron in certain quantum Hall states or the emergence of monopoles in spin ice. In this talk, I will discuss the fractionalization of magnetic moments in a certain class of Mott insulators, in which the emergent degrees of freedom are Majorana fermions that form an (almost) conventional metal. The origin of such a dichotomous state is elucidated by a family of exactly solvable models of frustrated quantum magnets in three dimensions, which might be realized in a class of recently synthesized Iridate compounds. These models thereby provide the first analytical tractable examples of long sought-after quantum spin liquids with a spinon Fermi surface and even an entire new class of quantum spin liquids - a so-called Weyl spin liquid, in which the fractionalized degrees of freedom form a topological semi-metal.

Energy waste is a severe bottleneck in the supply of sustainable energy to any modern economy. Besides developing new energy sources, the global energy crisis can be alleviated by re-utilizing the waste heat. In this talk, I will first introduce some background of harnessing the thermal energy by the thermoelectrics, spin caloritronics, and phononics. Then, in the second part, I would like to share with you some of my recent discoveries about the rectification and negative differential spin Seebeck effects, exemplified in metal/magnetic insulator interfaces and magnon tunneling junctions. These properties lead us to the novel devices, such as thermal-driven spin diode and transistor in the absence of electric transports. I call them spin Seebeck diode and transistor. These findings imply that a spin computer driven by waste heat might not be a dream in the future, which offer us new opportunities to achieve the smart control of energy and information at nanoscale.

Recent experimental developments in diverse areas - ranging from cold atomic gases over light-driven semiconductors to microcavity arrays - move systems into the focus, which are located on the interface of quantum optics, many-body physics and statistical mechanics. They share in common that coherent and driven-dissipative quantum dynamics occur on an equal footing, creating scenarios without immediate counterpart in condensed matter. A key challenge is to identify universal macroscopic phenomena, which manifestly witness microscopic non-equilibrium conditions. Here, we will report on three results in this direction. First, we show that dynamical Bose criticality in driven systems lies beyond the equilibrium Halperin- Hohenberg classification. Second, we argue that driven open systems in two dimensions, realized by ensembles of exciton-polaritons, cannot support superfluidity and quasi-long range order. Third, we reveal new, manifestly non- equilibrium scaling behavior in the short time heating dynamics of interacting, ultracold atomic quantum wires.

The output files of a digital camera are typically only 10% the size of the raw data. Can one design a physical process that only records the relevant information to begin with? The recently developed field of "compressed sensing" achieves this trick for certain signals. Building on tools from mathematical physics, we have introduced new methods to the theory which have since found applications in areas as diverse as face recognition, despeckling of movie frames, and large deviation bounds for non commutative processes. In a second, unrelated part, I will talk about the one-body quantum marginal problem. Here, the task is to decide which set of local reduced density matrices are compatible with a globally pure state. Known to be non-trivial since the 70s, only recent developments in symplectic geometry and asymptotic representation geometry have made the problem tractable. I will report on our work that connects these methods to the study of multi-partite entanglement and fermionic many-body systems. Lastly, I will mention some results related to the classification of time evolutions in discrete quantum lattice systems (otherwise known as quantum cellular automata).

Low dimensional structures combine pronounced surface effects with distinct many body interactions. Both affect material properties decisively, as they determine excitations and boundaries between different electronic as well as structural phases. Here, we discuss how the electronic structure of low dimensional materials can be understood based on microscopic theory along with three examples of how interactions affect material properties. First, we consider chemically functionalized graphene and show how doping triggers adsorbate phase transitions including tendencies towards sublattice symmetry breaking. Regarding the electrons in layered materials, local "Hubbard interactions" generally compete with large non-local Coulomb interactions. We will discuss the "two-faced" nature of these non-local interactions: while they contribute to strong renormalizations of electronic excitations, non-local Coulomb terms turn out to weaken ground state electronic correlations frequently. Finally, we will turn to quantum impurity problems and show how electronic interactions shape excitation spectra in magnetic nanostructures.

Over the past 25 years, the dynamical mean field (DMFT) formalism has been extended from fermionic Hubbard-type models to realistic multi-band materials, bosonic lattice systems and even quantum field theories. It has also been developed into a powerful and versatile tool for the study of nonequilibrium phenomena in correlated lattice models. I will provide an overview of the key developments in the field and explain the most recent addition to the DMFT family - the DMFT treatment of quantum field theories. In the second part of the talk I will discuss two predictions from nonequilibrium DMFT studies: the possibility to switch the Coulomb repulsion into an effective attractive interaction through the application of periodic electric fields, and the existence of nonthermal critical points, which control the relaxation dynamics of the antiferromagnetic or superconducting order parameter on intermediate time-scales.

To derive Anderson localization of light is one of the holy grails of our time. I show in this talk theoretical results derived by Vollhardt-Wölfle theory of photons in a novel time dependent approach. The results are given for 3D disordered, finite sized real world systems of poly-disperse powders consisting of TiO_2 Mie spheres. Signatures of  Anderson localized states, namely interference effects, are determined and they can be clearly distinguished from long living light-matter bound states as well as frequency converted photons and losses. Influences of different types of non-linear effects are discussed.

The human flu virus undergoes rapid evolution, which is driven by interactions with its host immune system. We describe the evolution of viral genomes in terms of a non-equilibrium statistical mechanics model. This model successfully predicts the evolution of influenza one year into the future. Thus, evolutionary analysis transcends its traditional role of reconstructing past history. This has important consequences for public health: evolutionary predictions can inform the selection of influenza vaccine strains. We discuss the conditions of predictability and its links to cooperative phenomena and universality. These links highlight the key role of statistical mechanics in making evolutionary biology a predictive science.

The dynamics in granular matter is inherently out-of-equilibrium, as time-reversal symmetry is broken by the energy loss during interparticle collisions. This presents challenges to both theory and experiment: Experimentally, granular systems need to be agitated strongly to achieve steady states or need to be measured in microgravity to avoid sedimentation. For the theoretical treatment, suitable ensembles need to be assumed or inferred from experiments. Experiments from parabolic-flight and drop-tower campaigns shall be shown for the dilute regime of granular gases where homogeneous steady states and granular cooling are observed. For dense granular fluids, the derivation of granular rheology from first principles shall be presented as well as new experimental techniques for the characterization of granular states such as X-ray radiography and tomography, and terahertz scattering.

Complex quantum systems out of equilibrium are at the basis of a number of the most intriguing puzzles in physics. This talk will be concerned with recent progress on understanding how quantum many-body systems out of equilibrium eventually come to rest and thermalise. The first part of the talk will highlight theoretical progress on this question, taking in several ways a quantum information view - employing ideas of Lieb-Robinson bounds, quantum central limit theorems and of concentration of measure. These findings will be complemented by experimental work with ultra-cold atoms in optical lattices, in setups constituting dynamical "quantum simulators", allowing to probe physical questions that are not only out of reach for state-of-the-art numerical techniques based on matrix-product states, but also relate to classically computationally hard problems.

There are two standard "Ising" models for the spreading of epidemics, the "SIS" (susceptible-infected-susceptible) epidemic and the "SIR" (susceptible-infected-removed) model. Both are related to percolation - the first to directed, the second to undirected - and thus both show continuous ("second-order") phase transitions when the conditions for spreading are critical. Recently, much interest has been roused by models which show first order transitions. After giving a short overview I will concentrate on first order transitions in models with cooperativity. This cooperativity can be of two very different types. On the one hand, several agents on neighboring nodes in a network (or sites on a lattice) can cooperate in infecting a new node (like three friends who convince you more easily than any single one of them to adopt a political opinion). On the other hand, also two pathogens (like HIV and TB) can cooperate in the sense that one of them lowers the resistance to the other. In the first case the transition from a continuous to a discontinuous phase transition is a standard tricritical point (with higher n-point interactions in a field theoretic formalism), while in the second one one has a multi-component order parameter. In several instances, the resulting first order transitions are actually "hybrid", i.e. they involve also features of second-order transitions like scaling. In one case, one even finds that two order parameter definitions which coincide for ordinary percolation display different transition orders.

A one dimensional spinless p-wave superconductor may be in a topological nontrivial state, in which it has a zero energy Majorana bound state at each end. Although no known materials are spinless p-wave superconductors, such a system can be realized in principle in spin-orbit coupled nanowires with proximity-induced pairing from a nearby s-wave superconductor. After introducing the topological phase, I will discuss how non-idealities, such as potential disorder and deviations from a strict one-dimensional limit, affect the topological phase and its signatures in a current-voltage measurement.

The entanglement spectrum, i.e. the logarithm of the eigenvalues of reduced density matrices of quantum many body wave functions, has been the focus of a rapidly expanding research endeavor recently. Initially introduced by Li & Haldane in the context of the fractional quantum Hall effect, its usefulness has been shown to extend to many more fields, such as topological insulators, fractional Chern insulators, spin liquids, continuous symmetry breaking states, etc. After a general introduction to the field we review some of our own contributions to the field, in particular the perturbative structure of the entanglement spectrum in gapped phases, the entanglement spectrum across the Mott-insulator transition in the Bose-Hubbard model, and the relation of the entanglement spectrum of (1+1) dimensional quantum critical systems to the operator content of their underlying CFT.

Because of spontaneous symmetry breaking and a mass gap, Dirac spectra show universal behavior that can be understood by means of random matrix theory. We discuss the effect of a nonzero lattice spacing on QCD Dirac spectra and find tail states that have been observed before in disordered condensed matter systems. Despite the Coleman-Mermin-Wagner theorem Dirac spectra also show universal behavior in two dimensions, but the unversality classes are different from those in four dimensions and depend on the parity of the lattice. A complete classification of two dimensional lattice QCD Dirac spectra in terms of the ten fold classification of random matrix theories is given.

In or close-to-equilibrium response to external stimuli and statistical forces are primarily entropic and governed by the standard thermodynamic potentials. We report on a program of identifying a unifying kinetic feature, called the frenetic contribution, to complement entropy considerations in the study of nonequilibrium behavior. We therefore present extensions of the first and second fluctuation-dissipation relation for driven systems or for probes in contact with nonequilibrium (active) baths.

Nanomechanical structures can be coupled to light in order to control their mechanical vibrations. Recent experimental developments in this field of "cavity optomechanics" have led to laser-cooling of such vibrations to their quantum ground state and entanglement between mechanics and the radiation field. A particularly promising platform consists in photonic crystal structures with optical and vibrational modes localized at defect sites. If these sites were to be arranged periodically, they would form an "optomechanical array" that can be described via a tight-binding model of interacting photons and phonons. I will describe our theoretical predictions, including light-induced synchronization of mechanical oscillators, quantum many-body dynamics of photons and phonons, Dirac physics on an optomechanical honeycomb lattice, and the possibility of generating artificial photonic gauge fields.

A theory of the scaling behavior of the thermodynamic, transport and dynamical properties of a three-dimensional metal at an antiferromagnetic (AFM) critical point is presented. It is show how the critical spin fluctuations at the AFM wavevector q = Q induce energy fluctuations at small q, giving rise to a diverging quasiparticle effective mass over the whole Fermi surface. The coupling of the fermionic and bosonic degrees of freedom leads to a self-consistent relation for the effective mass, which has a strong coupling solution in addition to the well-known weak-coupling spin-density wave solution. We thereby use the recently introduced concept of critical quasiparticles, employing a scale dependent effective mass ratio m*/m and quasiparticle weight factor Z. We specifically assume a scale dependent vertex correction boosting the coupling of fermions and spin fluctuations. The ensuing spin fluctuation spectrum obeys E/T-scaling. Our results are in good agreement with experimental data on the heavy fermion compounds YbRh2Si2 and CeCu6-xAux assuming 3D and 2D spin fluctuations, respectively.

The assignment of adequate probabilities to the basic outcomes of some random experiment under consideration is a prerequisite of a probabilistic description. The maximum entropy principle of Statistical Mechanics solves this problem by stating that among all probability distributions that satisfy some given constraints the one of maximum Boltzmann-Gibbs-Shannon entropy must be chosen. Being an indisputable principle of Statistical Mechanics, its status outside physics as a general method of statistical inference is less clear. We present a foundation of the maximum entropy principle that is based on probabilistic arguments. It deliberately avoids reference to notions of information and it does not appeal to physically motivated properties of entropy. This is achieved by formalizing probability assignment as a certain symmetric, continuous mapping that additionally satisfies a condition of self-consistency. We show that any such mapping can be expressed as a variational principle, i.e. as a generalized maximum entropy principle with an a priori unspecified entropy function. Adding a condition of statistical independence, an earlier result of Shore and Johnson shows that the entropy function must be essentially the standard Boltzmann-Gibbs-Shannon entropy.

Boundary entropy of boundaries in one-dimensional critical systems was defined by I. Affleck and A. Ludwig in 1991. A classic example of such systems is a conduction defect at low temperature as described by the Kondo model. Boundary entropy has a number of peculiar properties, for example it can be negative. In this talk we will discuss how this quantity is defined and what are its known properties.

In 2006 the phenomenon of Bose-Einstein condensation at room temperature was discovered in a ferromagnet YIG (Yttrium-Iron garnet) by the group of experimenters from University of Münster leaded by S. Demokritov. They also presented a theoretical explanation of their experiment. In my talk I will first describe this experiment and its explanation. Recently (June 2012) the same group discovered a low-contrast interference pattern in the intensity of Brillouin light scattering. The spectrum of spin waves in a thin film of YIG has two minima at finite values of momentum + Q and -Q. The interference demonstrates that the two condensates have very different densities despite complete symmetry of the system to space inversion. In our work (Fuxiang Li, W.M. Saslow and V.L. P.) we propose a theory explaining why and how this symmetry is violated. Our theory predicts that in thinner films it is possible to observe a symmetric state of condensates. The transition between these two states can be driven by magnetic field. The theory also predicts a new type of the collective oscillations. The dipolar interaction plays a special role trapping the sum of the two condensate phases at the values 0 or pi. Transition between these two states is possible in non-symmetric phase and can be observed as a cusp in the plot of contrast vs. magnetic field.

In this talk,‭ ‬the low-energy quantum transport properties of the Coulomb-Majorana junction‭ ‬will be discussed,‭ ‬where several helical nanowires are coupled to a joint mesoscopic superconductor with finite charging energy.‭ ‬By virtue of the proximity effect,‭ ‬Majorana bound states are formed near the ends of the superconducting wire parts,‭ ‬which are coupled together by charging effects.‭ For sufficiently weak but finite charging energy,‭ ‬this system generically approaches an isotropic SO(M‭) ‬Kondo fixed point with non-Fermi liquid behavior observable in quantum transport observables such as the temperature-dependent conductance tensor or the fluctuating current noise correlator.‭ ‬The latter quantities follow from the Keldysh formulation of an effective phase action approach.‭

Interacting particle systems in biology, chemistry and the social sciences are traditionally described by ordinary or partial differential equations. These are purely deterministic and based on the assumption that effects of noise can safely be neglected. Such approaches are no doubt chosen for their mathematical simplicity, the theory of differential equations is well developed, whereas existing theories of non-equilibrium stochastic dynamics are more complex and largely incomplete. In this talk I will consider systems of a finite number of interacting particles, their intrinsic stochasticity can then no longer be ignored. I will discuss noise-induced phenomena such as quasi-cyles, quasi-Turing patterns and travelling quasi waves, and explain how they can be characterised analytically within the so-called linear noise approximation. Examples where this is relevant include systems in evolutionary dynamics, game theory and chemical reaction systems. One focus of the talk will be on models with delay dynamics, important for example in gene regulatory systems or in epidemiology. I will show how path-integral approaches can be used to derive general results for their chemical Langevin equation and linear-noise approximation.

Before cell division, two identical copies of chromosome need to be segregated accurately. Each chromosome is connected to a "nano-ring" (dam1) by "rods" (Ndc80). For accurate chromosome segregation, the two chromosomes are pulled apart in the opposite directions by two sets of "nano-hooks", formed by microtubules (MTs), that are inserted into these rings. An externally applied tension can lead to detachment of the hooks from the ring; the mean lifetime of such an attachment is essentially a mean first-passage time. Recent pioneering in-vitro experiments with reconstituted nano hook-ring device established that the mean lifetimes of such attachments vary non-monotonically with increasing tension. In this talk I'll explain the counter-intuitive stabilization of the attachments by small tension with a unified model that we have developed very recently. The catch-bond-like mechanism emerges naturally in this model from the interplay of tension-dependence of (i) the potential landscape and (ii) MT depolymerization rate. I'll also show how the distribution of lifetimes of the hook-ring attachment depends on (a) the structure, (b) energetics, and (c) kinetics of the coupling.

Quantum technology is maturing to the point where quantum devices, such as quantum communication systems, quantum random number generators and quantum simulators, may be built with powers exceeding the performance of classical computers. A quantum annealer, in particular, finds solutions to hard optimization problems by evolving a known initial configuration towards the ground state of a Hamiltonian that encodes an optimisation problem. In this talk I will present results from experiments on a 108 qubit D-Wave One device based on superconducting flux qubits and will provide evidence that the device indeed performs quantum anealing. To assess the computational power of the quantum annealer I compare it to optimised classical algorithms and will present first preliminary results for a D-Wave Two system with more than five hundred qubits.

Biological evolution is a fascinating subject which can be fully understood only if it is approached from many different angles. In this talk I will present my personal point of view on how physics can advance our understanding of biological evolution. I will focus on three problems in the evolution of bacteria I have been working on recently. I will begin with a simple, statistical-physics model of the evolution of antibiotic resistance. This is a timely and important problem because drug-resistant, pathogenic bacteria are becoming a major health hazard. I will show that resistant bacteria can rapidly emerge in environments with spatially non-uniform drug concentration such as our bodies during antibiotic treatment. Towards the end of my talk, I will briefly discuss the evolution of metabolic networks in bacteria and biological evolution in bacterial colonies growing on solid substrates.

The interplay of spin-orbit coupling and correlations opens a new playground to study a variety of effects ranging from helical Luttinger liquids to quantum spin systems generated by threading pi-fluxes through correlated topological insulators. In this talk, I will concentrate on the Kane-Mele model supplemented by a Hubbard U. After discussing the salient features of the non-interacting model - topological invariants and edge states - I will concentrate on the above mentioned correlations driven effects. The results obtained are based on large scale quantum Monte Carlo simulations which turn out to be free of the infamous sign problem for this specific class of models.

In this talk I will briefly review the basic principles of electromagnetic field quantisation in the presence of macroscopic matter, and explain its relevance to the quantum interaction between (isolated) microscopic particles and macroscopic surfaces. As a first example, I will review some aspects of propagation of nonclassical light through absorbing optical devices. I will then concentrate on two aspects of atom-surface interactions --- decoherence and dispersion forces (Casimir, Casimir-Polder and van der Waals forces). Both effects can be understood within the framework of macroscopic QED as spatially dependent relaxation processes and line shift mechanisms, respectively. I will present examples of highly excited atoms and weakly bound molecules that are particularly susceptible to changes in dispersion forces.

We give an introduction to the area of gauge/gravity duality and its applications. Based on string theory, gauge/gravity duality maps strongly coupled quantum field theories to weakly coupled gravity theories and thus provides a new framework for studying physical phenomena in strongly coupled systems. We describe the main features of this approach and discuss its range of applicability. Moreover, we give examples of applications in both elementary particle/nuclear physics and condensed matter physics. The examples presented include the quark-gluon plasma, mesons, quantum phase transitions as well as superfluids and superconductors.

Quantum point contacts are elementary building blocks of numerous semiconducting nanodevices. Despite their simple structure, however, their conductance properties exhibit anomalous features, collectively known as the "0.7-anomaly", whose origin is still subject to controversial discussions. We offer a detailed microscopic explanation for the 0.7-anomaly and the zero-bias peak that typically accompanies it: the common origin of both is a smeared van Hove singularity in the local density of states at the bottom of the lowest one- dimensional subband of the point contact, which causes an anomalous enhancement in the Hartree potential barrier, magnetic spin susceptibility and inelastic scattering rate. We present theoretical calculations and experimental results that show good qualitative agreement for the dependence of the conductance on gate voltage, magnetic field, temperature, source-drain voltage (including the zero-bias peak) and interaction strength. For low energies we predict and observe Fermi-liquid behavior analogous to that known for the Kondo effect in quantum dots. At high energies, however, the analogy between 0.7-anomaly and Kondo effect ceases to be applicable.

Non-equilibrium quantum systems represent one of the most promising possibilities for realizing novel states of matter. I will consider the non equilibrium situation known as quantum quench, in which a closed system evolves from an initial state that is not a Hamiltonian eigenstate such as those achieved by suddenly switching a control parameter. An important question is under what conditions the system reaches a stationary state and in which circumstances this state is characterized by an effective “thermal”, i.e. equilibrium, distribution. I will discuss how to obtain the time evolution of observables and correlation functions with a variety of theoretical techniques including quantum field theory (in particular CFT) and integrability. These approaches allow to have a rather complete understanding of the relaxation dynamics and the most challenging open problems will be presented.

A major problem of quantum field theory in curved spacetime, and quantum gravity more generally, is the lack of sufficient observational and experimental guidance. To address this issue I am proposing to explore various phenomena of semi-classical gravity and quantum gravity in table-top experiments. The overall programme is based on the existence of analogue gravity models for semi-classical quantum gravity, demonstrating that certain effects predicted within quantum field theory in curved spacetimes can be mimicked in easy-to-access physical systems, such as fluids and superfluids. In addition, I will explore the possibility of adapting the general principles underlying analogue gravity models to full quantum gravity, combining tools and concepts from quantum information theory with discrete quantum gravity. In contrast to many other proposals in quantum gravity, the project objectives are not only theoretical (analytical and numerical studies), but also of experimental nature. The specific scientific goals are to study the robustness and universality of (rotating) black hole phenomena in water channel flows, cosmological particle production in Bose-Einstein condensate, and the emergence of a smooth geometry as an ensemble average of binary encodings of triangulated manifolds.

In many cases, interacting fermions in one spatial dimension are described by the Luttinger model of free bosonic density excitations. Due to the absence of an interaction between these bosonic degrees of freedom, the model is integrable. As a consequence, it does not relax back to equilibrium when one excites it via the local injection of electrons. Instead, it reaches a non-equilibrium steady state with a peculiar electronic distribution function and spectral density. In the case of two co-propagating chiral channels, the non-perturbative method of non-equilibrium bosonization allows to characterize the electron distribution by a fractional Fano factor and interpret it in terms of charge fractionalization.

We study the superconducting proximity effect in a quantum wire with broken time-reversal (TR) symmetry connected to a superconductor. We consider the situation of a strong TR-symmetry breaking, so that Cooper pairs entering the wire from the superconductor are immediately destroyed. Nevertheless, some traces of the proximity effect survive: for example, the local electronic density of states (LDOS) is influenced by the proximity to the superconductor, provided that localization effects are taken into account. With the help of the supersymmetric sigma model, we calculate the average LDOS in such a system. The LDOS in the wire is strongly modified close to the interface with the superconductor at energies near the Fermi level. The relevant distances from the interface are of the order of the localization length, and the size of the energy window around the Fermi level is of the order of the mean level spacing at the localization length. Remarkably, the sign of the effect is sensitive to the way the TR symmetry is broken: In the spin-symmetric case (orbital magnetic field), the LDOS is depleted near the Fermi energy, whereas for the broken spin symmetry (magnetic impurities), the LDOS at the Fermi energy is enhanced.

Many out-of-equilibrium systems undergo an instability when an order parameter is suitably tuned, giving rise to well known and widespread processes: growth, convection, phase separation, and so on. A common feature is the emergence of a nontrivial spatial structure, whose typical scale L may display different dynamics. We are specially interested in understanding when L increases in time (coarsening process) and how. Using a continuum modelling and a multiscale approach, for several equations we are able to obtain a phase diffusion equation describing the dynamics of the emerging pattern and to predict when and how coarsening proceeds.

Active motion of particles in aqueous solution may lead to interesting collective phenomena such as pattern formation or macroscopic fluid flows. I will discuss two examples where this can be observed. First, I will present lattice Boltzmann simulations of a microscopic model for cytoplasmic streaming in algal cells. Here, myosin motors entrain the surrounding fluid by walking along actin filaments while dragging vesicles or other organelles. I will pay particular attention to how the high speeds observed in experiments can be achieved by assuming a layer of lower viscosity at the outer wall of the simulated compartment. The second example is a system of sedimenting self-propelled particles with the additional property of bottom-heaviness, which results in a tendency of particles to swim upwards. I will give analytical results for the dilute limit and numerical results for the interacting case where particles form vortices and columns.

In two dimensional topological phases of matter, processes depend on gross topology rather than detailed geometry. Thinking in 2+1 dimensions, particle world lines can be interpreted as knots or links, and the amplitude for certain processes becomes a topological invariant of that link. While sounding rather exotic, we believe that such phases of matter not only exist, but have actually been observed in quantum Hall experiments, and could provide a uniquely practical route to building a quantum computer. Possibilities have also been proposed for creating similar physics in systems ranging from superfluid helium to strontium ruthenate to semiconductor-superconductor junctions to quantum wires to spin systems to cold atoms.

Power grids, which form the cornerstone our technical infrastructure, will undergo a revolutionary change in the upcoming decades driven by the advancement of renewable energy sources. Large centralized power plants are put out of operation in favor of many small, distributed and potentially fluctuating generators. To face this enormous challenge for the reliable operation of the power grid, both the structure and control of the grid must undergo a radical change. This development must be supported by a great advancement of our theoretic understanding of complex networked systems. In this talk I discuss the collective dynamics of power grids using an idealized oscillator model that model grid dynamics on coarse scales. This model bridges the gap between abstract large-scale, basically structural network models from physics on the one hand and detailed simulations of small electric engineering systems on the other. I analyze self-organized synchronization of the grid depending on the network topology and study the impact of dynamical perturbations and the influence of topological changes. I find that, contrary to common intuition, the addition of new transmission lines may reduce the overall grid capacity and explain this phenomenon by geometric frustration in the oscillator model.

In an introductory part I will discuss the relation between topological insulators and the architectural challenge of building a bridge between Hongkong and mainland China. Then I discuss how a magnetic field induces one-dimensional edge channels when the two-dimensional surface states of three-dimensional topological insulators become gapped. Remarkably, the Hall effect remains quantized even in situations, where the theta-term characteristic of the bulk and the associated surface Hall conductivities are not quantized due to the breaking of time-reversal symmetry. The quantization arises as the theta-term changes by integer multiples along a loop around n edge channels. Model calculations show how an interplay of orbital and Zeeman effects leads to quantum Hall transitions, where channels get redistributed along the edges of the crystal. The network of edges opens new possibilities to investigate the coupling of edge channels. In a last part I will shortly discuss aspects of strongly disordered topological insulators as well as interaction effects on the surfaces.

"Stochastic resetting" is a rather common process in everyday life. Consider searching for some target such as, for example, a face in a crowd or one's misplaced keys at home. A natural tendency is, on having searched unsuccessfully for a while, to return to the starting point and recommence the search. In this talk I explore the consequences of such resetting on perhaps the most simple and common process in nature, namely, the diffusion of a single or a multiparticle system. It turns out that a nonzero rate of resetting has a rather rich and dramatic effect on the diffusion process, strongly affecting the behaviour of mean first passage times and survival probabilities.

I will present recent results on a one-dimensional wire with strong Rashba and Dresselhaus spin-orbit coupling (SOC), which supports Majorana fermions when subject to a Zeeman magnetic field and in proximity of a superconductor. By introducing a new local quantity dubbed as "Majorana polarization", I will argue that it can be used as a local order parameter to characterize the topological transition between a trivial system and a system exhibiting Majorana bound modes. We have found that the local "Majorana polarization" is correlated to the transverse spin polarization, and we propose to test the presence of Majorana fermions in a 1D system by a spin-polarized density of states measurement. Such quantity turns out to be very useful to analyze one-dimensional topological SN and SNS long junctions obtained by placing a topological insulating nanowire in the proximity of either one or two superconducting finite-size leads: for a finite-size SN junction the Andeev Bound States (ABS) spectrum exhibits a zero-energy extended state which carries a full Majorana fermion, while the ABS of long SNS junctions with phase difference pi transform into two zero-energy states carrying two Majorana fermions.

Tumor growth is a multifactorial process that surely emerges from molecular and genetic abnormalities, but also depends strongly on cell-cell and cell-extracellular matrix macroscopic regulations and interactions. Numerous models have been developed to understand the mechanisms controlling solid tumor morphogenesis: While the earliest efforts were focusing on cell proliferation kinetics, modulated by the availability of supplied nutrients, new approaches emphasize the crucial role of several biophysical processes, including local matrix remodeling, active cell migration and traction, and reshaping of the host tissue blood vessel network. In this talk a brief review over a number of representative models will be given, in particular those predicting the emergence of invasive behavior through growth instabilities at the tumor-host interface. Then the focus will be put on the analysis of vascular remodeling during tumor growth within a theoretical model including angiogenesis, cooption and regression of blood vessels. The physical mechanisms determining the morphological and hydrodynamical characteristics of the emerging tumor vasculature are analyzed and implications for blood borne drug delivery are discussed.

The description of non-Fermi liquid metals is one of the central problems in the theory of correlated electron systems. I present a holographic theory which builds on general features of the thermal entropy density and the entanglement entropy. Remarkable connections emerge between the holographic approach, and the postulated strong-coupling behavior of the field theory.

The development of thermodynamics in the second half of the 19th century has had a strong impact on both technology and natural philosophy. It is true that the steam engine for the conversion of heat into work existed before thermodynamics was developed as a branch of physics. However, the systematic theory improved the conversion process, and it succeeded in developing other processes essential to modern life, notably refrigeration and rectification. So, altogether thermodynamics has provided humanity with cheap energy, and cheap fuel, - consequently with cheap, and abundant, and unspoiled food. Thus thermodynamics has made populations grow, and life expectancy increase beyond anything people could possibly have imagined 200 years ago. At the same time thermodynamics has uncovered the precarious balance between determinism and stochasticity which is essential to processes on earth, including life. The competition of those intentions is described by the doctrine of energy and entropy in thermodynamics; energy tends to force a system into one single state, and entropy tends to spread the system evenly over all possible states. These competing tendencies are weighed by temperature such that minimal energy determines cold systems and maximal entropy determines hot systems.

The origin and development of cracks in earth materials is a subject of general interest and wide application: from seismologists studying earthquakes to engineers studying the strength of materials. Therefore many laboratory experiments have been carried out to investigate the response of rocks to an applied differential stress, often using acoustic emissions (AE) to track intermittent crack growth inside the rock specimen prior to system-sized sample failure. Under a constant applied stress in double-torsion tensile tests with a guide groove and a single dominant crack, independent observations of the stress intensity factor and crack growth velocity imply the size of the largest (sub-) critical crack grows with time t according to an inverse power-law. A similar law holds for the mean crack length in a population of micro-cracks growing under compressional stress with no pre-defined fault plane, often treated using mean field models that ignore localisation of damage clearly seen in the experiments. Here I present a new hypothesis for the origin of this formula by combining expressions for crack population growth and localisation in a single model. The model is tested and some of its parameters inferred from analysis of the AE rate and the spatial clustering of its source locations from laboratory data.

States of matter are conventionally classified according to broken symmetries. Topologically ordered phases fall outside of this paradigm: with no local order parameter, they nevertheless have many peculiar properties setting them apart from disordered phases. In 2D, such phases may support anyons - quasiparticles that are neither bosons nor fermions. Moreover, anyons with non-Abelian statistics are expected to occur in certain fractional quantum Hall systems as well as materials supporting topological superconductivity (intrinsic or induced). In this talk, I will discuss various approaches designed to detect such exotic statistics. I will also describe our recent proposal for novel physical systems supporting unusual non-Abelian anyons. I will also mention potential applications of such systems for topological quantum computation.

A milestone in graphene research was the 2005 discovery of an integer quantum Hall effect. In contrast to its manifestation in conventional two-dimensional (2D) electron systems, such as in semiconductor heterostructures, the graphene quantum Hall effect reflects the "ultra-relativistic" character of the underlying carriers, via a particular sequence of plateaus in the transverse Hall resistance. In view of the fractional cousin of the integer quantum Hall effect in 2D electron systems, one may thus naturally ask the question about a fractional quantum Hall effect in graphene. Does it also reflect the ultra-relativistic character of the charge carriers? To what extent is it different from the fractional quantum Hall effect in (non-relativistic) semiconductor heterostructures? Many of these questions remain open from an experimental point of view, although some fractional states have recently been observed in transport and spectroscopic measurements. This talk aims at a theoretical perspective on the fractional quantum Hall effect in graphene, namely in view of its multi-component character due to the fourfold spin-valley degeneracy, which gives rise to an internal SU(4) symmetry and that is approximately respected by the underlying electron-electron interactions. This theoretical perspective will be confronted with recent experimental advances.

This talk concerns the rigorous derivation of diffusion, thermalization and decoherence in simple quantum systems: a spin or a particle interacting with phonons. Our approach takes the Markovian description (Pauli master equation or quantum Boltzmann equation) as a starting point. However, since such a Markovian description is only valid in a certain scaling limit (vanishing coupling constant and long time), we develop an expansion around the Markovian description to control the behavior at finite coupling constant. This expansion consists of a controlled renormalization group flow with Brownian motion as the fix-point solution. The long-range nature of the velocity-velocity correlation function is an example of a physical quantity that is not described correctly within the Markovian description (cfr. Alder-Wainwright), but that is captured by our approach.

In this talk, I will discuss mechanisms by which (nonlinear) quantum systems effectively 'thermalize' into long time stationary distributions. Focusing on the paradigmatic example of the Dicke model (a large spin coupled to a boson mode), I will demonstrate how a constructive description of the thermalization process is facilitated by the Glauber Q or Husimi function, for which the evolution equation turns out to be of Fokker-Planck type. The equation describes a competition of classical instabilities and quantum diffusion. By this mechanism the system follows a "quantum smoothened" approach to equilibrium, which avoids the notorious singularities inherent to classical chaotic flows. I will touch upon the relevance of the above picture to recent experiments in cold atom physics.

Statistics of energy levels in Hamiltonian systems with classically chaotic dynamics belong to one of three Wigner-Dyson symmetry classes. By the semiclassical approach this remarkable universality can be attributed to the systematic correlations between actions of periodic orbits. The correlating periodic orbits do not exist as independent individuals but rather come in closely packed bunches. We demonstrate how this bunching phenomena can be rigorously described using symbolic dynamics of the system. For systems with Markov partition we introduce an ultrametric distance between periodic orbits and organize them into clusters. Each cluster is composed of periodic orbits passing through (approximately) the same points of the phase space. We then study the distribution of cluster sizes in the asymptotic limit of long trajectories. In the case of the baker's map this problem turns out to be equivalent to the one of counting degeneracies in the length spectrum of de Bruijn graphs.

We study the welfare effects of social security in an overlapping generations general equilibrium model with aggregate and idiosyncratic risk. Prior research on social security has only considered either aggregate or idiosyncratic risk. We show analytically that the aggregate and idiosyncratic risks interact due to the life-cycle structure of the economy. This interaction increases the welfare gains of a marginal introduction of an unfunded social security system. Adding a second interaction by making the variance of the idiosyncratic risk countercyclical further increases the welfare gains. In our quantitative experiment, raising the contribution rate from zero to two percent leads to long-run welfare gains of 3.5% of life-time consumption on average, even though the economy experiences substantial crowding out of capital. Approximately one third of these gains can be attributed to the interactions between idiosyncratic and aggregate risk.

Noise is ubiquitous in dynamical systems. Its impact on the dynamics can be quite versatile, ranging from bad signal-to-noise ratios to qualitatively new phenomena such as oscillations of populations, which would be absent without noise. Here "noise" stands for stochastic fluctuations of various origin. Of particular interest are stochastic fluctuations in the context of biology. What is their role in evolutionary processes or in the living cell as the basic unit of life? We shall focus on a dynamical unit which consists of only two species interacting in a non-linear way. This unit may be regarded as a coarse-grained description of a genetic circuit. For comparison we shall first discuss the unit in a deterministic description and then turn to a fully stochastic one. There we shall unravel the effect of demographic fluctuations and fluctuations in the reaction times. The power spectrum will show which source of stochastic behavior is dominant. We shall compare analytic predictions with Gillespie simulations. The results raise an interesting generic question about oscillatory genetic systems observed in nature.

The emergence of topological order is one of the most intriguing phenomena in quantum many-body physics and one of possibly far reaching relevance - topological quantum matter is increasingly appreciated as possible medium for quantum computation purposes. In this talk, I will discuss the stability of topological quantum matter when considering the effects of interactions and disorder on the collective quantum state formed by a set of topological excitations, so-called anyons. In particular, I will discuss the formation of a thermal metal of Majorana fermions in a two-dimensional system of interacting non-Abelian anyons in the presence of moderate disorder. This bulk metallic phase occurs for various proposed systems supporting Majorana fermion zero modes when disorder induces the random pinning of a finite density of vortices. This includes all two-dimensional topological superconductors in so-called symmetry class D. A distinct experimental signature of the thermal metal phase is the presence of bulk heat transport down to zero temperature. I will finish by discussing implications for topological quantum computing proposals. 

We analyze the low-energy excitations of diluted Josephson-junctions arrays, XY-quantum antiferromagnets, and interacting bosons near the percolation threshold. We then show that the critical behavior of these systems is dramatically altered by the presence of a Berry phase that leads to an order parameter precession and, depending on the system, is caused by an external magnetic field or an external gate voltage. Most interestingly, the low energy excitations become spinless fermions with a fractal spectrum. As a result, critical properties not captured by the usual Ginzburg-Landau-Wilson description of phase transitions emerge, such as complex critical exponents, log-periodic oscillations and dynamically broken scale-invariance. [Rafael M. Fernandes, Jörg Schmalian, Phys.Rev.Lett.106, 067004 (2011)]

We consider multiple quantum dots or molecular junctions in the single-electron tunneling regime which, due to a high degree of spatial symmetry, have a degenerate many-body spectrum. As a consequence, interference phenomena which cause a current blocking can occur at specific values of the bias and gate voltage. We present here necessary and sufficient conditions for interference blockade also in the presence of spin-polarized leads. As an example we analyze a benzene single-electron transistor. For a setup with parallel polarized leads, we show how to exploit the current blocking to selectively prepare the system in a defined spin state without application of any external magnetic field.

The Einstein – Hilbert action of General Relativity is not fit to describe quantum fluctuations of the metrics as it does not restrict either large fluctuations or fast varying ones. Therefore, it defines at best an effective theory which, of course, is tremendously successful. A hint how to construct a true and well defined `microscopic’ gravitation theory is provided by the fact that there are fermions in Nature. Fermions require that the field variables to be used are the vierbein and the Lorentz spin connection. This leads to Cartan’s formulation of General Relativity, but field fluctuations are not restricted there either because none of the possible general covariant action terms is sign-definite. A way out is to present the vierbein as a bilinear "current" of more fundamental fermion (spinor) fields. Path integrals over Grassmann variables are well defined for whatever sign of the fermion action. We suggest that in the ultraviolet limit quantum gravity possesses only spinor and gauge field degrees of freedom, like in the Standard Model. The theory can be easily regularized by putting it on a space lattice. It is explicitly invariant under local Lorentz transformations and, in the continuum limit, under diffeomorphisms. It is a theory that is well-behaved at small distances, and quantum fluctuations are well defined. We discuss how to check if Newton’s law is reproduced in the infrared limit in the world with fluctuating metrics. Our formulation of quantum gravity allows its unification with the Standard Model, and that will be also briefly discussed.

Non-intersecting random walkers (or ''vicious walkers'') have been studied in various physical situations, ranging from polymer physics to wetting and melting transitions and more recently in connection with random matrix theory or stochastic growth processes. In this talk, I will present a method based on path integrals associated to free Fermions models to study such statistical systems. I will use this method to calculate exactly the cumulative distribution function (CDF) of the maximal height of p vicious walkers with a wall (excursions) and without a wall (bridges). In the case of excursions, I will show that the CDF is identical to the partition function of 2d Yang Mills theory on a sphere with the gauge group Sp(2p). Taking advantage of a large p analysis achieved in that context, I will show that the CDF, properly shifted and scaled, converges to the Tracy-Widom distribution for $\beta = 1$, which describes the fluctuations of the largest eigenvalue of Random Matrices in the Gaussian Orthogonal Ensemble.

In this talk, I discuss long-term memory in nature (particularly in climate) and its implications for the occurrence of extremes. I also show how external trends can be estimated in records with long-term memory and apply the results to the estimation of anthropogenic global warming.

Under the influence of external fields a large variety of materials and systems shows complex hysteretic behavior. The latter means that in addition to major hysteresis loops, one finds many subloops or minor loops, if the external field is reversed or oscillates at some intermediate values. Well-known examples range from adsorption in porous media to the magnetization of magnetic materials. Such a behavior is traditionally described by so-called hysteresis operators, for which the Preisach operator is one of the most prominent representatives. Correspondingly, the interaction of such hysteretic systems with its environment is naturally described by operator-differential equations. Despite its importance the dynamics resulting from such equations is not well understood. In this talk I will review the working principles of the Preisach hysteresis operator and its applications. Subsequently recent results on dynamical systems with such hysteretic subsystems will be presented. They range from the appearance of 1/f-noise under simple input-output conditions to the co-existence of infinitely many attractors for operator-difference or operator-differential equations describing e.g. the motion of an iron sample in an inhomogeneous magnetic field.

I will briefly review some recent developments on how to achieve and manipulate effective gauge fields for ultracold atoms. Starting with some historical remarks on effective gauge theories in molecular and time-dependent systems, I move on to show how this translates to ultracold atoms exposed to spatially varying laser fields. This research has gained great attention lately, and the experimental efforts are seriously beginning to pay off. At the present, the non-Abelian case has not been experimentally demonstrated but will in the near future... An important example of a non-Abelian gauge potential is the one of Rashba, which for a particular choice of atom-laser configuration can be constructed in these systems. This opens the door for sudies of effects such as, spin Hall currents, relativistic Zitterbewegung, half quantized vortices. Combined with optical lattices, there's even hope to explore quantized Hall physics and interesting physics that comes with it.

Computing marginals of probability distributions (magnetizations, spin-spin correlations etc) is an important problem in statistical physics of disordered systems and many other fields. In decision problems one typically wants to estimate the likelihood that a single variable takes a given value, given the interactions with all the other variables, then fix that variable to its most likely value, and so estimate the most likely configuration of all the variables. An important technical application is decoding in communication systems, where the task is to estimate the code word most likely to have been sent from the recieved signal and what one knows about the channel. In principle one can compute the marginals of any Markov chain by Monte Carlo, but such methods are inherently slow for large systems. Over the last decade there has therefore been intense interest in approximate methods to compute marginals of probability distributions deterministically (the cavity method, Belief Propagation, iterative decoding), which overall work by nodes (representing variables) sending messages between each other and so collectively yield sometimes exact and often very good estimates of the marginals. In the language of physics all these methods compute a variational ansatz of the Boltzmann-Gibbs free energy of an equilibrium statistical mechanical system where the messages are related to Lagrange multipliers. I will describe recent work on extending message-passing from computing the stationary states of Markov chains obeying detailed balance to Markov chains which do not. This "dynamic cavity method" works to some extent, and in particular outperforms dynamic mean-field methods on standard kinetic (non-equilibrium) Ising systems. This is joint work with Hamed Mahmoudi (2011a-c), building on earlier work by Montanari and co-workers (2009) and Neri and Bolle (2009).

I will discuss the physics of transport phenomena in driven chaotic environments (`kicked rotors'), as realized in recent atom optic experiments. The behavior of these systems depends sensitively on the value of a scaled Planck constant \tilde h: for irrational values of \tilde h/(4\pi) they fall into the universality class of disordered electronic systems and I will discuss the corresponding localization phenomena. In contrast, for rational values the rotor-Anderson insulator acquires an infinite conductivity and turns into a `super-metal'. This implies the existence of a novel 'metal/super-metal' quantum phase transition in cold atom systems.

The discreteness of biological components, whether they be proteins in a cell or individuals in an ecological population, has important consequences for the dynamics of biological systems. This concept is quite natural for statistical physicists, but not widely recognised in the life sciences. I will discuss some examples relevant to cell biology, cancer progression, and embryo development, in which stochastic process theory along with agent-based computer simulations have helped provide new insights and understanding.

We propose a general classification of nonequilibrium steady states in terms of their stationary probability distribution and the associated probability currents. The stationary probabilities can be represented graph-theoretically as directed Cayley trees; closing a single loop in such a graph leads to a representation of probability currents. This classification allows us to identify all choices of transition rates, based on a master equation, which generate the same nonequilibrium steady state. We explore the implications of this freedom, e.g., for entropy production, and provide a number of examples.

A general scheme for the construction of exact ground states of correlated electron models will be discussed. It consists of three steps: The transformation of the Hamiltonian into positive semidefinite form, the construction of many-particle ground states of this Hamiltonian, and the proof of the uniqueness of these ground states. This approach works in any dimension, assumes no integrability of the model and only requires sufficiently many microscopic parameters in the Hamiltonian. Thereby ground states of diamond Hubbard chains are constructed which exhibit a multitude of properties such as flat-band ferromagnetism and correlation induced metallic, half-metallic or insulating behavior. Furthermore, the exact ground state of a 1D periodic Anderson model is shown to explain the unusual ferromagnetism in the f electron material CeRh3B2. Finally, it is proved that pentagon chain polymers may be designed to become ferromagnetic or half metallic.

In this talk, we will describe a mechanism that generates oscillations in simple stochastic models of epidemic dynamics. We will show that, first, intrinsic (demographic) stochasticity can generate large coherent fluctuations which behave as sustained oscillations and that, second, the power spectrum of these fluctuations can be calculated analytically using the system size expansion. The application of this analysis to the problem of the modeling of recurrent epidemics shows that, in systems whose sizes represent real populations, the role of stochastic effects becomes fundamental for the interpretation of historical data.

The Kondo effect is a classic paradigm in condensed matter theory, which describes the dynamic screening of a quantum impurity embedded in a metallic host. The underlying renormalization group (RG) description of such problems is by now very well understood. But comparatively little is known in real-space: while a length-scale associated with the screening process has been proposed theoretically, its physical interpretation remains controversial. We demonstrate that as one moves away from the impurity, physical quantities evolve in a characteristic way, reproducing fully the RG flow between fixed points. Behaviour typical of each fixed point can thus be identified in distinct regions of space. The implications of these results are discussed in relation to the popular 'Kondo screening cloud' picture.

An important aspect for understanding the emergence of classical dynamics in a quantum mechanical framework is to explain the origin of super-selection rules observed at macroscopic scales. Two specific cases will be discussed, based on microscopically realistic master equations. In the first part, I will show how the distinction and stability of chiral molecular configuration states can be explained by decoherence. In the second part, the emergence and dynamics of motional pointer states will be explored, by associating them with the solitonic solutions of a nonlinear equation related to a particular stochastic unraveling of the appropriate master equation.

Traditionally, evolutionary game dynamics is described in terms of deterministic differential equations. In the past years, evolutionary game dynamics has benefitted from considering finite populations, which adds a natural source of noise. The intensity of selection, which corresponds to an inverse temperature, determines the interplay between selection and noise. Weak selection allows numerous new results in stochastic evolutionary game dynamics, but sometimes also strong selection allows analytical results. Theoretical aspects of this development will be discussed and examples from the evolution of cooperation and punishment will be given, where noise can become crucial for the dynamics.

The equations of the Ginzburg-Landau theory of superconductivity retain their mathematical fascination. The talk will discuss various results concerning the vortex solutions in two dimensions at the critical point between the Type I and Type II regime. Here vortices neither attract nor repel, so there are many static vortex and multi-vortex solutions. These also exist in curved background geometries. In a model where the vortices can move ballistically, one can study the effective mass of one vortex, what happens in vortex collisions, and the properties of an interacting gas of many vortices. There are some precise but surprising mathematical results here. Whether they have physical relevance is (at least for the speaker) an open issue.

At the glass transition, no thermodynamic anomalies or diverging length scales in static properties have been seen so far experimentally. On the other hand, dynamical correlation functions diverge at the transition and show rich features over many orders of magnitude in time. One approach to explain glassy dynamics is the framework of mode-coupling theory: The equations of motion for density correlation functions in a fluid are approximated self-consistently and in the long-time limit yield glass- transition singularities. Such singularities are known from caustics in optics (e.g. seen in rainbows and coffee mugs), and in fluids they explain many features in glassy dynamics. In addition to liquid-glass transitions, the theory predicts glass-glass transitions. These glass-glass transitions are a consequence of the mathematical structure of the theory, and their experimental confirmation therefore lends credibility to the theory. The mathematical features and dynamical predictions of the theory shall be demonstrated with data from colloidal suspensions, liquid water, and static granular matter.

Systems of low dimensions have provided special opportunities, challenges, and fascination for condensed matter physicists. Issues of long-range order, dimensional crossover, and instabilities are all significant in such systems. In this Talk, I provide a pedagogical overview of my theoretical research in relation to low-dimensional electron systems ranging from nano “zero-dimensional” systems to (quasi) twodimensional systems such as high-Tc superconductors, graphene, topological insulators and novel oxide heterostructures. We shall also spend some time on onedimensional systems which are described by the Tomonaga-Luttinger paradigm. Finally, I show that condensed matter concepts can also be applied to cold atoms in optical lattices and photon systems.

The carbon atoms in graphene (Nobel Prize in Physics 2010) form a honeycomb lattice which gives rise to many of the peculiar physical properties of this fascinating material. Dictated by the interaction with the ions of the lattice, the low energy electrons in graphene have the same dispersion relation as mass-less Dirac fermions. We will discuss interesting physical phenomena of Dirac fermions in graphene such as Klein tunneling, transport through evanescent modes, and consequences of the spectrum on quantum computing devices based on graphene quantum dots. Furthermore, we will address another in some sense even richer condensed matter system that shows Dirac fermion physics: Topological insulators (TIs) behave like usual insulators in the bulk but like metals at the boundaries. This gives rise to Dirac fermions at the edge of a TI. In nature, TIs have been first realized in HgTe/CdTe quantum wells (in 2D) and later on also in 3D in BiSb, BiSe, as well as BiTe crystals. We will discuss interesting physical properties of 2D TIs where spin and charge properties of the system are ultimately locked to each other.

Much effort has been devoted recently to the search for experimental demonstrations of Majorana fermions and the exotic quantum statistics that can be encoded by them. In this talk I will mainly focus on Majorana fermions in the non-abelian quantum Hall state at filling fraction nu=5/2. To detect them, there have been several proposals for transport experiments in the linear regime, which however are not robust with respect to disorder in realistic samples.  I will discuss signatures of Majorana states in non-linear transport through a Coulomb blockaded antidot of nu=5/2 quantum Hall fluid surrounded by an integer quantum Hall state.  In contrast with linear Coulomb blockade (CB), current-voltage characteristics in the non-linear regime of the CB hold information of the many-particle excitation spectrum of the system. A peak in the differential conductance dI/dV will appear whenever a proper resonance condition between the source-drain voltage and the excitations of the dot is met. The "diamond structure" that characterizes the CB out of the linear response regime could serve to identify the nature of the nu=5/2 state.