Equilibration and GGE for hard wall boundary conditions

TL;DR

This paper analyzes the long-term behavior of a Lieb-Liniger gas with hard wall boundaries after a quench, demonstrating the applicability of GGE and quench action approaches and relating the eigenstates to a doubled periodic system.

Contribution

It establishes a connection between the long-time eigenstates of a hard wall Lieb-Liniger gas and a doubled periodic system, extending GGE and quench action methods to boundary conditions.

Findings

Time averages correspond to eigenstates related to doubled systems.

GGE and quench action approaches are valid for long-time local correlations.

Local operators far from boundaries have identical expectations as in the doubled system.

Abstract

In this work we present an analysis of a quench for the repulsive Lieb-Liniger gas confined to a large box with hard wall boundary conditions. We study the time average of local correlation functions and show that both the quench action approach and the GGE formalism are applicable for the long time average of local correlation functions. We find that the time average of the system corresponds to an eigenstate of the Lieb-Liniger Hamiltonian and that this eigenstate is related to an eigenstate of a Lieb-Liniger Hamiltonian with periodic boundary conditions on an interval of twice the length and with twice as many particles (a doubled system). We further show that local operators with support far away from the boundaries of the hard wall have the same expectation values with respect to this eigenstate as corresponding operators for the doubled system. We present an example of a quench where the gas is initially confined in several moving traps and then released into a bigger container, an approximate description of the Newton cradle experiment. We calculate the time average of various correlation functions for long times after the quench.