Global large time dynamics and the generalized Gibbs ensemble

TL;DR

This paper investigates the long-time behavior of large quantum systems after a sudden quench, showing that the Gibbs ensemble describes global observables in generic systems, while the generalized Gibbs ensemble applies to certain integrable systems.

Contribution

It clarifies the conditions under which the Gibbs and generalized Gibbs ensembles accurately describe the large time dynamics of quantum systems post-quench.

Findings

Gibbs distribution captures global observable dynamics in generic large quantum systems.

Generalized Gibbs ensemble accurately describes integrable systems with noninteracting fermionic degrees of freedom.

Conditions for local quantities to be described by GGE are less restrictive but not systematically analyzed.

Abstract

We study the large time dynamics of a macroscopically large quantum systems under a sudden quench. We show that, first of all, for a generic system in the thermodynamic limit the Gibbs distribution correctly captures the large time dynamics of its global observables. In contrast, for an integrable system, the generalized Gibbs ensemble captures its global large time dynamics only if the system can be thought of as a number of noninteracting uncorrelated fermionic degrees of freedom. The conditions for the generalized Gibbs ensemble to capture the large time dynamics of local quantities are likely to be far less restrictive, but this question is not systematically addressed here.