Session F01: Plenary Talk - Victor Galitski

Many-Body Quantum Chaos and Emergence of Statistical Mechanics

Both our everyday experience and laboratory experiments indicate that physical systems, initially prepared in a non-equilibrium state, time-evolve into thermal equilibrium. Sets of axioms have been formulated to justify this generic behavior and the emergence of statistical mechanics. Yet, there is no clear understanding of the fundamental principles underlying the universality of thermalization and ergodicity. How do such irreversible thermal states emerge in quantum systems, which are governed by the "reversable" unitary laws of quantum physics? This talk will review recent work on this topic and the closely related field of many-body quantum chaos. It will first introduce the basic notions of classical and quantum chaos in single-particle systems. We will consider different facets of quantum chaoticity such as universal distribution of energy levels and the quantum butterfly effect. Then, the concept of many-body quantum chaos will be defined using the former approach rooted in celebrated random matrix theory. It will be briefly discussed how this theory can be derived from first principles, which will lead to a surprising observation that small non-unitary perturbations strongly affect the resulting theory. It suggests the key conclusion of our recent work that spontaneous breaking of unitarity may be responsible for the emergence of chaos in interacting many-body systems.