Department of Physics • University of Cologne

Physical law imposes important constraints for virus structure, replication and spread. Here we discuss how it can help to better understand the different stages of the viral life cycle. Most viruses use a spherical protein shell to protect their genome; its assembly has to avoid kinetic trapping and malformed structures, a process that can be analyzed with statistical models for self-assembly. Many viruses, including SARS-CoV-2, influenza A and Ebola, are in addition wrapped by a membrane which anchors the glycoproteins attaching them to the host cells. Continuum models can be used to identify the physical limits of the entry process, including the minimal size and typical time required for entry. For enveloped viruses, the most critical step in the life cycle is the opening of a fusion pore, to release the genome into the host cell. Continuum models can be used to calculate the corresponding free energy landscape and to identify strategies to prevent this last step of the infection.

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.

Inducing superconductivity in topological materials stimulates the formation of novel quantum states of matter. Besides the original prediction in 3D topological insulators, the notion of topological phases has been generalized to different dimensions and extended to the higher-order states. In the last few years, our research has demonstrated the possibility of realizing the topological superconductivity in engineered 3D topological insulators [1], 3D Dirac semimetals [2,3], and their 1D hinge states. Particularly, Cd3As2 is predicted to be a higher-order topological semimetal, possessing three-dimensional bulk Dirac fermions, two-dimensional Fermi arcs [4], and one-dimensional hinge states [5] or non-Hermitian states [6]. These topological states have different characteristic length scales in electronic transport. We show that the superconducting proximity effect can also be a sensitive probe for distinguishing these states. [1] B. de Ronde, et al., Nanomaterials 10, 794 (2020). [2] Li, C. et al. Nat. Mater. 17, 875 (2018). [3] Wang, A. Q. et al. Phys. Rev. Lett. 121, 237701 (2018). [4] Li, C.-Z. et al. Nat. Communications. 11, 1150 (2020). [5] Li, C.-Z. et al. Phys. Rev. Lett. 124, 156601 (2020). [6] Wang, A.Q. et al. Submitted (2022)

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.

Remarkable experimental progress in quantum simulation enabled studies of non-equilibrium phenomena in interacting quantum systems. Bringing quantum matter out-of-equilibrium is a tool to engineer desired properties, but theoretically poses a major challenge, due to the exponential growth of computational complexity. I will overview theoretical progress in describing non-equilibrium quantum matter, based on quantum entanglement. In particular, I will describe mechanisms to avoid thermalisation, which lead to coherence protection and enable non-equilibrium phenomena not envisioned within statistical mechanics. Understanding spatial and temporal entanglement out-of-equilibrium suggests new efficient computational methods and provides a unifying principle for classification of non-equilibrium phases.

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.