Exact time evolution of space- and time-dependent correlation functions after an interaction quench in the 1D Bose gas

TL;DR

This paper provides an exact analysis of the non-equilibrium dynamics of the 1D Bose gas after an interaction quench, revealing relaxation behaviors and validating the generalized Gibbs ensemble for long-time predictions.

Contribution

It presents an exact calculation of correlation functions' time evolution after an interaction quench in the Lieb-Liniger model, demonstrating the ensemble's predictive power.

Findings

Different correlation functions relax differently over time.

The generalized Gibbs ensemble accurately predicts long-time averages.

The study confirms the ensemble's validity across all length scales.

Abstract

We consider the non-equilibrium dynamics of the interacting Lieb-Liniger gas after instantaneously switching the interactions off. The subsequent time evolution of the space- and time-dependent correlation functions is computed exactly. Different relaxation behavior is observed for different correlation functions. The long time average is compared with the predictions of several statistical ensembles. The generalized Gibbs ensemble restricted to a fixed number of particles is shown to give correct results at large times for all length scales.