Quantum chaos, integrability, and weak ergodicity breaking
ABSTRACT
In isolated chaotic quantum systems, any subsystem gets gradually entangled with its complement. Consequently, the equilibrium behavior of any local observable is well described by the Gibbs ensemble. In contrast, equilibration in integrable systems cannot be described by conventional statistical mechanics. In this talk, I will discuss the statistical properties of the disordered chaotic and integrable quantum systems in terms of energy correlations, Hilbert space structure and quench dynamics. Importantly, the survival probability (the overlap between the initial and time-evolved state) shows a slope-dip-ramp-plateau structure where the ramp indicates the long-range correlations present in the energy spectrum. Such dynamical signatures of chaos can be detected in present day quantum simulators. Finally, I will discuss weak ergodicity breaking from kinetic constraints in many-body systems, which lead to persistent oscillations for certain initial states despite the occurrence of thermalization at infinite temperature.
