Equilibration of a Tonks-Girardeau gas following a trap release

TL;DR

This paper provides an exact solution for the non-equilibrium dynamics of a Tonks-Girardeau gas after trap release, demonstrating equilibration to a generalized Gibbs ensemble in the thermodynamic limit.

Contribution

It presents an exact analytic solution for the many-body dynamics and proves equilibration to a generalized Gibbs ensemble for a Tonks-Girardeau gas.

Findings

Reduced density matrix converges to a generalized Gibbs ensemble

Equilibration mechanism is universal for 1D systems

Analytic solution applicable in thermodynamic limit

Abstract

We study the non-equilibrium dynamics of a Tonks-Girardeau gas released from a parabolic trap to a circle. We present the exact analytic solution of the many body dynamics and prove that, for large times and in a properly defined thermodynamic limit, the reduced density matrix of any finite subsystem converges to a generalized Gibbs ensemble. The equilibration mechanism is expected to be the same for all one-dimensional systems.