### Mathematics Colloquium

**Marcos Rigol
**

Pennsylvania State University

**Title:** From unitary dynamics to statistical mechanics in isolated quantum systems

**Date:** Friday, September 02, 2022

**Place and Time:** Zoom, 3:05-3:55 pm

**Abstract.**

Experiments with ultracold gases have made it possible to study dynamics of (nearly) isolated quantum many-body systems, which has revived theoretical interest on this topic. In generic isolated systems, one expects nonequilibrium dynamics to result in thermalization: a relaxation to states where the values of macroscopic quantities are stationary, universal with respect to widely differing initial conditions, and predictable through the time-tested recipe of statistical mechanics. However, it is not obvious what feature of a many-body system makes quantum thermalization possible, in a sense analogous to that in which dynamical chaos makes classical thermalization possible. Underscoring that new rules could apply in the quantum case, experimental studies in one-dimensional systems have shown that traditional statistical mechanics can provide wrong predictions for the outcomes of relaxation dynamics. We show that isolated "nonintegrable" systems do in fact relax to states in which observables are well-described by statistical mechanics. Moreover, we argue that the time evolution itself only plays an auxiliary role as thermalization occurs at the level of individual eigenstates.