Information theoretic concepts in thermodynamics, QM and QFT

Entropy bridges the gap between information theory and statistical physics. More precisely the entropy formula by Shannon (picture left) and Gibbs coincide up to a factor (which is Boltzmann's constant) and the maximum entropy prinicple allows to interprete the fundamental principle of thermodynamics as a consequence of maximal missing information. Also many quantities from information theory play an important role in the understanding of quantum mechanics (QM): E.g. quantum mutual information, quantum Fisher information, or entanglement entropy. Here I'm focusing especially on relative entropy, which turns out to be a very useful concept in different scenarios: It introduces are more natural way of thinking about information as it always refers to a certain model description, has a meaningful continuum limit and UV divergencies in a quantum field theoretic (QFT) setting when computing entanglement entropies are absent. Moreover I'm interested in information geometry and how elementary objects as e.g. the Fisher information metric are related to physical questions.

Models of analog gravity

It is well-known that very cold bosons can form a Bose-Einstein condensate (BEC), i.e. a state where almost all bosons occupy the ground state of a quantum system. This effect allows to observe quantum phenomena on a macroscopic scale. In a quantum field theoretic setting one can describe a BEC as the non-relativistic limit of a weakly-interacting scalar QFT. Small perturbations lead to the notion of phonons, which are the quasi-particles of the underlying quantum field. Interestingly there exist strong relations between cold atoms and cosmology: Phonons in a BEC act like particles in spacetime, s.t. phenomena from cosmology can be mimicked by cold atoms in the laboratory. Of special interest are analogons of the FRW universe and the Schwarzschild black hole (so-called acoustic or sonic black hole). In particular I work on the questions how external and internal potentials have to be shaped and to which extent the usual approximations are justified in order to produce the former mentioned situations in actual experiments.

Physics of event horizons

Horizons are one of the most astonishing phenomenons in modern physics. They can be imagined as boundaries in spacetime that restrict information transfer. The most prominent examples are black holes, a certain class of solutions of Einstein's field equations. When thinking about horizons the two former mentioned topics come together: A quantum field theoretic approach suggests the existence of Hawking radiation, which is an effect of quantum entanglement across the boundaries of a horizon. Many unsolved problems appear in this context, e.g. the black hole information paradox. In my work I try to tackle physical questions by using quantum information theoretic concepts in quantum field theory.