Thermalization and Quantum Chaos

Abstract

Ergodic and chaotic motion in phase space was identified by Boltzmann as the key prerequisite to attain thermal equilibrium in classical many-body systems more than a century ago. The transcription of this notion to the realm of quantum mechanics has still remained a matter of lively debate. Does an isolated quantum many-body system initially prepared in a non-stationary state thermalize and, if so, what are the signatures and time scales of the approach to equilibrium? Moreover, can the notion of classical-quantum correspondence be extended to the concepts of ergodicity and chaos in statistical mechanics? Is the breakdown of quantum integrability and the appearance of quantum chaos as signified by universality classes of level statistics necessary to attain thermalization? In this talk, I will discuss the interplay between quantum chaos and the emergence of the thermal state for a prototypical isolated Fermi-Hubbard many-body system. Such systems have become accessible in experiments with ultracold gases. We analyse the thermal state by determining the reduced one-particle density matrix (1RDM) of an impurity embedded in the Fermi-Hubbard system. Employing an exact diagonalization of the entire N-particle (impurity + bath) system we establish the direct connection between quantum chaos and the approach of the 1RDM to the canonical ensemble. *Work in collaboration with Mahdi Kourepaz, Fabian Lackner, Stefan Donsa and Iva Brezinova