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Thursday, May 07, 2015
12:30 PM - 1:30 PM
T-DO Conference Room

Quantum Lunch

From unitary dynamics to statistical mechanics in isolated quantum systems

Marcos Rigol
Pennsylvania State University

Recently, experiments with ultracold gases have made it possible to study dynamics of (nearly) isolated many-body quantum systems. This has revived theoretical interest on this subject. 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 statistical mechanics can provide wrong predictions for the outcomes of relaxation dynamics. Analyzing specific examples, we argue that generic isolated quantum systems do in fact relax to states in which observables are well-described by statistical mechanical [1,2]. Moreover, we show that time evolution itself plays a merely auxiliary role as thermalization happens at the level of individual eigenstates. We also discuss what happens at integrability points, where a different set of rules apply [3,4].

[1] M. Rigol, V. Dunjko, and M. Olshanii. Thermalization and its mechanism for generic isolated quantum systems. Nature 452, 854 (2008).
[2] M. Rigol, Breakdown of Thermalization in Finite One-Dimensional Systems, Phys. Rev. Lett. 103, 100403 (2009)
[3] M. Rigol, V. Dunjko, V. Yurovsky, and M. Olshanii. Relaxation in a Completely Integrable Many-Body Quantum System: An Ab Initio Study of the Dynamics of the Highly Excited States of 1D Lattice Hard-Core Bosons. Phys. Rev. Lett. 98, 050405 (2007).
[4] A. C. Cassidy, C. W. Clark, and M. Rigol. Generalized Thermalization in an Integrable Lattice System. Phys. Rev. Lett. 106, 140405 (2011).

Host: Sebastian Deffner