Quench dynamics of a Tonks-Girardeau gas released from a harmonic trap

TL;DR

This paper analytically studies the non-equilibrium quench dynamics of a Tonks-Girardeau gas released from a harmonic trap, showing convergence to a generalized Gibbs ensemble and analyzing entanglement entropy evolution.

Contribution

It provides an exact analytical solution for the dynamics of a Tonks-Girardeau gas after release from a trap, including correlation functions and entanglement entropy behavior.

Findings

Reduced density matrix converges to a generalized Gibbs ensemble.

Entanglement entropy reaches a simple stationary form.

Dynamics described explicitly for large times and thermodynamic limit.

Abstract

We consider the non-equilibrium dynamics of a gas of impenetrable bosons released from a harmonic trapping potential to a circle. The many body dynamics is solved analytically and the time dependence of all the physically relevant correlations is described. We prove that, for large times and in the thermodynamic limit, the reduced density matrix of any subsystem converges to a generalized Gibbs ensemble as a consequence of the integrability of the model. We discuss the approach to the stationary behavior at late times. We also describe the time-dependence of the entanglement entropy which attains a very simple form in the stationary state.