Many-Body Quantum Processes at the Edge of Chaos:From Non-Equilibrium Thermodynamics towards Quantum Gravity

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During the recent years a novel field in theoretical physics has emerged at the interface of statistical physics, quantum dynamics in atomic and condensed matter and cosmology, which can be subsumed under the topic many-body quantum chaos. Many systems from all these distinctly different areas have in common that they reside at the semiclassical border between many-body classical chaos and quantum physics, in fact in a two-fold way: (i) Far-out-of-equilibrium quantum dynamics involves high-energy excitations, associated with the usual short-wavelength limit where wave mechanics approaches the limit of classical particles; (ii) alternatively, the thermodynamic limit of large particle numbers N, where quantum fields pass into nonlinear waves, can also be regarded as semiclassical, governed by an effective Planck constant 1/N. These two complementary crossover regimes in state-of-the-art many-body physics that are experimentally relevant and theoretically particularly challenging, are central to this proposal and form the background for two methodically intimately connected major research streams:(i) I propose to develop a theory of thermo-scattering-dynamics, i.e., to probe quantum non-equilibrium processes through scattering. Developing a fundamental relation between the density of states and the scattering time delay of open many-body systems I will be able to directly connect thermodynamic observables to microscopic dynamical scattering properties, implying for instance to measure temperature or entropy by means of scattering times. Moreover, this opens up the intriguing possibility to monitor quantum thermalization processes, or mechanisms inhibiting them such as many-body localization, from the outside. This challenging program requires a general theory for the many-body density of states of N indistinguishable interacting particles.(ii) I propose a quantum chaos approach to quantum field theory, in particular to consider quantum gravity through the lense of many-body semiclassics. I will explore how classical and quantum field theories do diverge and predict associated many-body interference phenomena. In this respect, notably, two seemingly disconnected fields in physics, quantum chaos and quantum gravity, seem to have strong common links as signaled by striking analogies. Hence, I aim at establishing a connection between topological expansions in quantum gravity (associated with "baby-universes") and periodic-orbit theory in quantum chaos, based on a dynamical mechanism for emergent geometrical structures that I conjecture. This will contribute to a cross-fertilization of these disjoint fields. During the last years my group has developed a conceptually novel platform that provides powerful many-body tools enabling us, together with international experts, to enter these uncharted territories and to address such fundamental questions that have emerged at the interface between the classical and quantum many-particle world.