Department of Physics • University of Cologne

Karch-Randall-Sundrum (KRS) braneworlds have recently enjoyed a resurgence in popularity as they offer insights into the physics of black hole evaporation, particularly in higher dimensions. Since no well-controlled derivation of these model from string theory or supergravity is available, open questions remain about the consistency and existence of these models. In this talk, I will discuss aspects of the consistency of these models from the "bottom up".

We investigate how the efficiency of E. coli chemotaxis depends on the external environment and the internal biochemical pathway of the E.coli cell. When the cell is in a medium where the nutrient is diffusing and the form of nutrient profile is Gaussian, we find that there exists an optimal width of the profile for which the search time becomes minimum. In the case when the nutrient diffusion and cell movement occurs over comparable time-scales, there exists an optimum value of the nutrient diffusivity for which the search time becomes minimum. The simulation results in a phenotype model agree well with our analytical calculations in a related coarse-grained model. In a single cell chemotaxis the internal biochemical pathway involves noise due to the fluctuations present in the number of different molecules taking part in the reactions. This noise plays a very crucial role on the chemotactic performance of E. coli bacterium. We find that in the long time limit the localization and the uptake, i.e. the total nutrient intercepted along its trajectories, becomes maximum for an optimum value of the noise strength. We discuss a simple mechanism to explain this effect.

The final state of a spherically symmetric star always admits a singularity at its center if only gravitational effects are considered. This singularity is covered by an event horizon in most cases. However, the existence of singularities in final theory of Quantum Gravity is so far unclear. For some initial conditions to the matter distribution it is possible that the formed singularity might be temporary visible. This case is called a naked singularity and is of central interest in this thesis. Their existence implies the breakdown of General Relativity itself, since it manifests that future is unpredictable from initial data alone. Anything could form in the central singularity due to the presence of an infinitely large energy density. It was shown that initial conditions leading to naked singularities are physically meaningful and cannot be neglected. The following question arises: Are singularities an artifact of General Relativity itself and can be resolved by taking quantum mechanical effects into account? Here we show, that for a specific model containing a naked singularity, we obtain an everywhere vanishing wave function. This result can be interpreted as the avoidance of the classically allowed naked singularity. Furthermore, our toy model shows certain similarities to the Friedmann-Lemaitre-Robertson-Walker metric (FLRW metric). We show that a specific perturbation around this solution is also quantum mechanically forbidden. Our results demonstrate that canonical quantization is at least in our case capable of contributing to the ongoing debate on singularity avoidance. However, we consider only one case of a naked singularity and a result the general case of (naked) singularities still remains unclear.

We combine geometric data analysis and stochastic methods for data driven modeling of complex systems with application to finance. We identify low dimensional dominating variables and extract their stochastic models directly from the data. We identify and analyze quasi-stable states of the market.

One of the strong connection between the quantum information theory and the black hole physics is based on the conjecture of interpreting entanglement entropy as the black hole entropy, which passed various numerical tests. In the present talk, we add yet another strong supportive evidence to this conjecture, that is we numerically show that the temperature of entanglement is same as the Hawking temperature of black hole for massless free scalar fields. Also we show the validity of the first law of black hole mechanics using entanglement entropy and temperature.

In the canonical quantization of fields on curved space-time, the definition of the vacuum state is of fundamental importance. We consider the definition of vacuum states for scalar and fermion fields on rotating Minkowski and anti-de Sitter space-times. The construction of the vacuum state for a fermion field is much less constrained than for a scalar field. We explore the consequences of this freedom for the definition of rotating thermal states.

We show that in the first order gravity theory coupled to axions, there exist new kind of instanton configurations (solutions of Euclidean equations of motion) whose instanton number can be interpreted as the torsional Nieh-Yan topological index. These torsional pseudoparticles turn out to be the Giddings-Strominger wormholes. Importantly, these instantons are shown to induce tunneling between degenerate topological vacua in gravity theory, leading to a rich vacuum structure exactly similar to the famous theta vacuum of gauge theories. This nonperturbative quantum vacuum is characterised by a topological vacuum angle, which can be identified with the Barbero-Immirzi parameter. We conclude with a discussion on how this nonperturbative vacuum structure in quantum gravity, hitherto unnoticed, could have important implications in the context of cosmology and various parity violating phenomena in particle physics. In particular, based on this framework, we propose a possible solution to the cosmological constant

We consider Kaluza-Klein (KK) models where internal spaces are compact Einstein spaces. These spaces are stabilized by background matter (e.g., monopole form-fields). We perturb this background by a compact matter source (e.g., the system of gravitating masses) with the zero pressure in the external/our space and an arbitrary pressure in the internal space. We show that in the case of curved Einstein spaces, the Einstein equations are compatible only if the matter source is smeared over the internal space and perturbed metric components do not depend on coordinates of extra dimensions. The latter means the absence of KK modes corresponding to the metric fluctuations. There are two possibilities to satisfy the gravitational tests. First, the gravitating source (e.g. our Sun) should have the black string equation of state in the internal space. This result does not depend on the size of the internal space. Second, if the equation of state in the internal space is arbitrary (e.g. dust like), then the size of the internal space should be small enough and radion is very massive particle.

In the first talk we have seen that Symplectic Geometrie is a generalization of Hamilton mechanics and gives us a way to describe and see the phase space in geometrical terms. In this continuation we will talk about several applications of mathematical theorems to physics, e.g. Gromov's theorem from 1985 and the problem of geometric quantization.

Orbital physics in excited bands of optical lattices After numerous advances in manipulation and detection techniques, cold atoms in optical lattices have become a primary candidate for studies of mesoscopic quantum phenomena. The possibility of accessing both the weakly and strongly correlated regimes, allows for investigation of a variety of phenomena which include quantum phase transitions. After a brief introduction to the field of cold atoms, here we will explore the physics in excited bands of optical lattices - the p band. Due to an additional orbital degree of freedom, the physics in the p band is qualitatively different from the physics of the usual systems in the ground band. We will start by defining these orbital states and describing mean field properties of the system, with particular emphasis on the condensation (in the p band) of a confined system. We will then move to the strongly correlated regime to show that under specific circumstances, the physics of bosons in the p band can be described by the spin-1/2 quantum XYZ Heisenberg model in an external field, that is one of the paradigmatic models in the study of quantum magnetism.

We introduce an action principle for a class of integer valued cellular automata and obtain Hamiltonian equations of motion. Employing sampling theory, these discrete deterministic equations are invertibly mapped on continuum equations for a set of bandwidth limited harmonic oscillators, which encode the Schroedinger equation. Thus, the linearity of quantum mechanics is related to the action principle of such cellular automata and its conservation laws to discrete ones.

The unification of the four fundamental forces remains one of the most important issues in theoretical particle physics. In this talk, I will first give a short introduction to noncommutative spectral geometry, a bottom-up approach that unifies the (successful) Standard Model of high energy physics with Einstein's General theory of Relativity. The model is build upon almost-commutative spaces and I will discuss the physical implications of the choice of such manifolds. I will show that even though the unification has been obtained only at the classical level, the doubling of the algebra may incorporate the seeds of quantisation. I will then briefly review the particle physics phenomenology and highlight open issues and current proposals. In the last part of my talk, I will explore consequences of the gravitational-Higgs part of the spectral action formulated within such almost-commutative manifolds. In particular, I will study modifications of the Friedmann equation, propagation of gravitational waves and the onset of inflation. I will show how current measurements (Gravity Probe B and pulsars) can constrain free parameters of the model. I will conclude with a short discussion on open questions.

The mechanical approach to cosmological problems inside the cell of uniformity represents a very promising scientific research direction in modern cosmology. It may be also associated with discrete cosmology in the nonrelativistic limit. In its framework the observable inhomogeneous Universe is described in the first order approximation with respect to its deviation from the averaged homogeneous FLRW one, the gravitational potentials of separate inhomogeneities (galaxies) are found and their relative motion (particularly, the motion of the Milky Way and Andromeda as well as the dwarf galaxies around our Local Group) is investigated in detail. It turns out that the characteristic features of scalar perturbations (including, for example, singularities in the places of gravitating masses locations and beyond them) are sensitive to spatial topology and composition of the Universe. Thus, the discrete cosmology screens powerfully different cosmological models and sheds light on the spacetime structure and its filling.

A covariant description of a generic electromagnetic medium requires a set of 36 independent parameters, instead of two ordinary material parameters, ε and μ. Such a set is arranged in a 4-th order constitutive tensor. Due to the group theory, this tensor is irreducibly decomposed into the sum of three independent sub-tensors. The first principal part is a substitution of the classical set of parameters. Two other tensors, skewon and axion, have no classical analogs and may represent some novel properties of media or artificial materials. In my talk, I will describe how the generalized covariant dispersion relation is derived. The result is in a correspondence with the formula proposed by Hehl, Obukhov and Rubilar. I define the notion of optic tensor (an analog of acoustic tensor from elasticity) and describe its properties. With this new device, I show some new results about the skewon modified media. The most visual outcome is a proof that in the skewon modified vacuum the wave propagation is necessary superluminal. It means that the skewon is probably forbidden in vacuum, but not in material media.

Since their introduction, theories with higher derivatives are unavoidable and frequently arise in different contexts. Hamiltonian formulation for Higher derivative theories become necessary and is discussed in the first order formalism. This Hamiltonian formulation is applied to the minisuperspace cosmology following from the geodetic brane gravity model introduced by Regge and Teitelboim. The analysis is done using the equivalent first order approach. The constraint algebra is shown to realize a truncated Virasoro algebra. The gauge generator containing the exact number of gauge parameters is constructed. Equivalence between the gauge and reparametrization symmetries has been demonstrated. Complete gauge fixed computations have been provided and formal quantization is indicated.

Gravity theory in four dimensions has three independent topological parameters. In the Lagrangian, these show up as coefficients of three topological densities, namely Nieh-Yan, Pontryagin and Euler. We analyse the Hamiltonian theory based on this generalized Lagrangian. The resulting theory develops a nontrivial dependence on all three parameters, and is shown to admit a SU(2) gauge theoretic interpretation with a set of seven first class constraints corresponding to three SU(2) rotations, three spatial diffeomorphism and one to evolution in a timelike direction. We also study how the topological parameters affect the gravity action with or without a cosmological constant for manifolds with boundaries. For both Dirichlet and locally AdS asymptotia, the Barbero-Immirzi parameter is shown to appear as the only independent topological coupling constant in the action principle. Our analyses indicate that there might be nontrivial implications of the topological parameters in the quantum theory of gravity.

The goal of the Asymptotic Safety program consists in finding a nonperturbatively renormalizable quantum field theory of gravity and analyzing its properties. The ideas, the motivation and the concepts of Asymptotic Safety will be explained in the first part of this talk. Then, we focus on Quantum Einstein Gravity in case spacetime has boundaries and consider a specific example of a renormalization group calculation including scale dependent boundary terms. In the third part I show the impact of these results on black hole thermodynamics.

Motivated by the phenomenology of traffic inside the Golgi apparatus of cells, we study a one-dimensional aggregation-fragmentation model in an open system where the total mass is not conserved due to influx and outflux at the boundaries. As influx is increased, the system undergoes a phase transition to an unusual condensate phase in which the total mass shows giant fluctuations as well as strong temporal intermittency, as in the turbulence phenomena. These properties are established analytically in the absence of fragmentation and numerically for non-zero fragmentation. We have also studied a multi- species generalisation of this model which allows for interconversion between different species: in a certain limit, the system exists in a phase characterised by formation of localised, indefinitely growing aggregates of different species in different regions of the system. The broad relevance of this sort of a model in the context of Golgi structure and traffic will be briefly discussed.

We would like to explain the basic mechanisms underlying fully interacting higher-spin theory, aiming at giving a flavor of Vasiliev’s equations. We will start from the linearised theory, explain the Fradkin-Vasiliev procedure for cubic interactions and arrive at Vasiliev’s equations if time allows.

Mass-energy equivalence principle is considered an important consequence of General Relativity. I will reverse the usual approach and take the validity of the mass-energy equivalence principle as a postulate within the non-relativistic mechanics. In the classical case this yields special and general relativistic time dilation effects (to lowest order) and Nordtvedt’s quantitative version of the Schiff’s conjecture – a relation between the violations of the universality of free fall and deviations from the gravitational redshift. However, these results do not necessarily extend to quantum mechanics. Various semiclassical extensions of the mass-energy equivalence principle will be presented that correspond to theories in which the free fall and/or the time dilation effects are modified in the presence of quantum effects. These theories in general violate Schiff’s conjecture, yet, in the scenario considered by Nordtvedt, they all agree with the classical result. I will explain this apparent “paradox” and derive a quantum version of the Nordtvedt’s relation from a fully quantum extension of the mass-energy equivalence principle. In the end I briefly discuss experimental scenarios that allow distinguishing between these various formulations of the mass-energy equivalence principle.

If we are given an electromagnetic medium tensor we can compute the speed of a propagating signal. For example, in a homogeneous medium we can compute the phase velocity using plane waves. A less well understood question is the converse: If we know the behaviour of phase velocity in all possible directions for an unknown medium, how much can we say about the anisotropic structure of that medium? In this talk we describe a number of results on this question in the setting of linear, local, and non-dissipative (skewon-free) media. In particular, we discuss the classification of medium tensors where wave propagation is determined by one or two Lorentz null cones.

I present an investigation of non-Gaussian fluctuations of complex classical Ginzburg-Landau (GL) order parameter fields. The transfer-matrix formalism enables an exact treatment of the non-Gaussian fluctuations. According to this formalism the generalized GL energy functional is considered as an energy associated with a particular order parameter configuration. Therefore the partition function can be represented as a functional integral over all possible configurations of the order parameters. In the cases of a single and two competing order parameters the functional integration is formally analogous to an eigenvalue problem of a single and two quantum particles in an an-harmonic potential respectively. To solve the problem we use such techniques as the path integral Monte Carlo and the Lanczos method. The results obtained via both techniques are compared with each other and with known results for the single order parameter case. Afterwards the results for the competing order parameters are computed.

Motivated by heterogeneous traffic flow with communicating and non-communicating vehicles, I will address a combinatorial problem in in my talk: if communicating vehicles can detect the vehicle ahead (and behind) by front (and rear) sensors, I ask how many non-communicating vehicles are on average detected by communicating ones. Relating the problem to a discrete random walk in one dimension with a fixed number of steps allows to determine the detected vehicles for both open and periodic boundary conditions as well as for the case where communicating vehicles detect both or only one neighboring vehicle(s). In the random walk picture, where the two vehicles types stand for steps in opposite directions, non-communicating vehicles are detected whenever the resulting path has a corner.

Weak gravitational lensing will be one of the key methods in the future of cosmology, for the determination of cosmological parameters. Its way of extracting statistical information from the formation of cosmic structures, poses a hybrid between the methods applied to the CMB and the ones applied to the matter density contrast, in the mathematical description. Since the deflection of light by mass through its gravity, does not distinguish between baryonic and dark matter, an increased sensitivity towards the latter one is expected, compared to the traditional sources of information, on a first point of view. Moreover through the application of tomographic binning in redshift space, it is also expected that weak lensing will offer profound insights into the late time evolution of cosmic structures, therefore allowing for a closer determination of parameters characterizing dark energy and neutrinos. At the moment several weak lensing surveys are planned. Among them the Large Synoptic Survey Telescope and the Euclid space probe. It is therefore important to a priori evaluate their sensitivities on the cosmological parameters of interest. A very nice way of doing this is through the Fisher matrix method.

States that describe thermodynamic equilibrium in the thermodynamic limit of infinite volume cannot be described by density matrices in vacuum Fock space because of their everywhere finite energy density. In the framework of algebraic quantum field theory on Minkowski spacetime, such states can be readily described as expectation functionals with certain analyticity properties. In curved spacetimes, a globally defined temperature cannot generally be expected to exist, if the metric is not static. Therefore the description of thermal states is more difficult in this case. This talk explores the proposed concept of local thermal equilibrium states and discusses problems that arise even for the free scalar field in simple spacetime models.

I would like to talk about the zero-temperature Glauber dynamics of a random-field Ising model on Bethe lattices. With a special initial condition, we can exactly derive a macroscopically closed evolution equation, which determines a dynamical phase diagram related to avalanche phenomena. I will mention a possible application of this analysis for epidemic networks.

By taking into account Kant’s scientific background in the pre-Critical writings, it is possible to show the impact of traditional paradoxes and dilemmas that grounded his cosmology and cosmogony. In the first part of my contribution, I shall expound the relevance of the Kepler and Halley’s riddle, better known as the starry-dark-sky paradox, which has been later discussed and formalized by Olbers in the 19th century. In the second part, I shall clarify which elements of Kant’s cosmology can be read as an answer to this riddle, involving a specific hierarchical structure of the universe, which is represented as an expanding sphere. In order to highlight this conception, I shall refer to the influence exerted by Sir William Herschel on Kant’s Critical writings on natural science and theory of matter, as well as to the development of Kant’s transcendental philosophy that provided useful tools in order to clarify and solve paradoxes and dilemmas of natural science.

We introduce scalar perturbations in a homogeneous and isotropic universe with compact spatial sections filled with a massive scalar field. The gauge freedom is then almost entirely removed by imposing two different sets of gauge-fixing conditions, which lead to consistent results. We quantize completely the model by combining a polymer representation for the homogeneous degrees of freedom and a Fock representation for the perturbations. Criteria of symmetry and unitary dynamics determine the latter uniquely. We also present an equivalent quantization in terms of gauge-invariant variables. Moreover, we propose a quantum implementation of the Hamiltonian constraint whose solutions are totally characterized by their initial value on the minimum-volume section.

Understanding the mutual interdependence between the behavior of dynamical processes on networks and the underlying topologies promises new insight for a large class of empirical networks. We present a generic approach to investigate this relationship which is applicable to a wide class of dynamics, namely to evolve networks using a performance measure based on the whole spectrum of the dynamics' time evolution operator. As an example, we consider the graph Laplacian describing diffusion processes, and we evolve the network structure such that a given sub-diffusive behavior emerges.

The structure of solutions of the geodesic equations in general axially symmetric space-times can be very complex and differs significantly from the plane conic sections of Newtonian gravity. Each space-time exhibits an individual set of geodesics which allows to conclude from the observation of orbits on the physical properties of the underlying space-time. The complete set of solutions of the geodesic equation in a given space-time can be studied most conveniently by using analytical methods. In the case of type D space-times with separable Hamilton-Jacobi equation the analytical solutions can be constructed in terms of elliptic or the more general hyperelliptic functions. In this talk the structure of orbits and the construction of analytical solutions will be exemplified in some type D space-times.

I will discuss the statistics of the number of records for N identical and independent symmetric discrete-time random walks. At each time step, each walker jumps by a random length drawn independently from a symmetric and continuous distribution. One has to distinguish between two cases: (I) when the variance of the jump distribution is finite and (II) when it is divergent as in the case of Levy flights. In both cases the mean record number grows universally with the square root of n for large n, but with a very different behavior of the amplitude in the two cases. For a finite variance I will argue, and this is confirmed by numerical simulations, that the full distribution of the record number converges to a Gumbel law for large n. In case II, numerical simulations indicate that the distribution of the record number converges, for large n and N, to a universal nontrivial distribution, independently of the Levy index. I also discuss an application of these results to the study of the record statistics of daily stock prices.

We present evidence supporting the weakly paired Moore-Read phase in the half-filled second Landau level, focusing on some of the qualitative features of its excitations. Based on numerical studies, we show that systems with odd particle number at the flux N_φ=2N-3 can be interpreted as a neutral fermion mode of one unpaired fermion, which is gapped. The mode is found to have two distinct minima, providing a signature that could be observed by photoluminescence (PL). In this context, we briefly review the role of skyrmion excitations in PL experiments. In the presence of two quasiparticles the same neutral fermion excitation is shown to be gapless, confirming expectations for non-Abelian statistics of the Ising model with degenerate fusion channels 1 and ψ.

We study the effect of thermal fluctuations on the topological properties of chiral p-wave superconductors. In particular, we allow for thermally excited topological defects – vortices and anti-vortices. We find that the topological degeneracy remains robust as long as topological excitations remain paired. Above the KT transition, disorder-driven low-energy modes give rise to either a thermal metal or a non-topological thermal insulating phase, which have a drastically different splitting of the topological degeneracy. We can relate these results from the point of view of localization-delocalization transition studied in the context of disordered superconductors breaking time-reversal and spin symmetry.

Using a numerically exact continuous-time quantum Monte Carlo impurity solver and the DCA cluster dynamical mean field method with cluster sizes up to 16, we have been able to access the superconducting phase of the two dimensional Hubbard model for parameters believed to be relevant to high temperature copper oxide superconductivity. We present results for the phase diagram, the gap to transition temperature ratio, and the interplay of the pseudogap and the superconducting gap. The gap results are obtained by direct inference from imaginary frequency data and analytically continued spectral functions. Work done in collaboration with Olivier Parcollet and Andrew J. Millis

A new formulation of quantum-classical hybrid dynamics is presented, which concerns the direct coupling of classical and quantum mechanical degrees of freedom - of interest for approximation schemes and for the foundations of quantum mechanics, in particular at the quantum-classical border. The present linear theory differs from the nonlinear ensemble theory of Hall and Reginatto, but shares with it to fulfill all consistency requirements discussed in the literature, while earlier attempts failed to do this. Our work is based on a representation of quantum mechanics in the framework of classical analytical mechanics, showing that notions of states in phase space, observables, Poisson brackets, and related canonical transformations can be naturally extended to quantum mechanics and generalized for quantum-classical hybrids (arXiv:1111.2276 and 1202.3448). Classically induced decoherence, backreaction, separable interactions, enlarged algebra of observables, (non)locality, and “free will” can be discussed here.

Bacteria perform various kinds of motion based on a variety of molecular mechanisms. We are studying the twitching motility of bacteria such as Neisseria gonorrhoeae, which use so called type IV pili to propel themselves over surfaces. Pili are long polymeric structures given out of the bacterial body which adhere to the surface and then retract, thus pulling the cell body. Recent experiments performed on these bacteria suggest that several pili co-operate in bacterial motion and that their co-ordination may be based on a tug-of-war between pili pulling in different directions. We are studying the Twitching Motility of bacteria, by a stochastic tug-of-war model, with a strong connection to experiments. The system is modeled by taking into consideration the stochastic nature of different processes. We describe the system as a tug-of-war between the pili, pulling a bacterium in different direction, to test whether this idea, together with known properties of individual pili can explain the observed patterns of bacterial motion.

It is now well-established that individual bacteria of many types switch stochastically between two phenotypes: fast-growing "normals" susceptible to antibiotics, and slowly-growing "persisters" hardly affected by the drug. In the competition of species during exponential growth, persisters are a burden, but they may become beneficial when introducing "stress" phases like drug treatment. We suggest to shift the focus to the persistence of an established population. Due to fluctuations, the population will (after a long time) eventually go extinct; persisters act as a life insurance against this. We study a simple stochastic model of these processes. Using a WKB approximation, we find the most likely path to extinction and quantify the extinction risk under both favorable and adverse conditions. Analytical results are obtained both in the biologically relevant regime when the switching is rare compared with the birth and death processes, and in the opposite regime of frequent switching. We explain how persisters strongly reduce the extinction risk and show that rare switches are most beneficial to this end.

In the inflationary scenario of loop quantum cosmology (LQC) in the presence of inverse-volume corrections, we study the power spectra of scalar and tensor perturbations convenient to confront with observations. Using the recent data of cosmic microwave background (CMB) and other cosmological experiments, for the first time we place experimental bounds on the LQC quantum corrections for several inflaton potentials.

The presentation treats the successful projection of the structure of classical fluids to effective pair potentials for a 2D system of super-paramagnetic colloids under a rotating external magnetic field. Knowing the structure of a system in form of the radial distribution function from experiments, the aim is to find a simple pair potential that reproduces the pair structure. To this end, a search algorithm was designed and implemented. It can seek for the right parameters of a given potential, resulting in the best fitting radial distribution function. It is shown that this combination works well for finding the right parameters of a superposition of a Lennard Jones Potential and a Yukawa Potential. This approach was extended to an anisotropic (patchy) potential in an effort to reproduce very unusual structures found in experiments, such as network chains including a number of Y-junctions.

Interfaces have been widely studied in the past few decades for their relevance in various domains: growing of thin films, vapor deposition, wetting, bacterial growth. In this talk I will caracterize the properties of the extremum of various types of interfaces. This central quantity refines our knowledge of the geometry of such objects. First I will consider equilibrated interfaces and present analytical results concerning the distribution of their Maximal Relative Height (MRH). Then, as an extension to disordered systems, I will consider the MRH of elastic interfaces in random media. The second part of the talk focuses on the growing regime in the KPZ universality class. Our analytical results on the non-intersecting Brownian motions model give new insights about this out of equilibrium system.