Interaction quench in a trapped one-dimensional Bose gas

TL;DR

This paper investigates the non-equilibrium dynamics of a one-dimensional Bose gas confined by hard walls after a quench from free to hard-core bosons, revealing how the system relaxes and retains memory of initial conditions.

Contribution

It provides a detailed analysis of the relaxation process and stationary states in a trapped 1D Bose gas following a quantum quench, highlighting differences from periodic systems.

Findings

Long-time density profile becomes uniform

Correlation functions retain initial state memory with algebraic decay

Stationary bosonic correlator decays exponentially at large distances

Abstract

We study the non-equilibrium quench dynamics from free to hard-core one-dimensional bosons in the presence of a hard-wall confining potential. We characterise the density profile and the two-point fermionic correlation function in the stationary state as well as their full time evolution. We find that for long times the system relaxes to a uniform density profile, but the correlation function keeps memory of the initial state with a stationary algebraic long-distance decay as opposite to the exponential behaviour found for the same quench in the periodic setup. We also compute the stationary bosonic two-point correlator which turns out to decay exponentially for large distances. We show that a two-step mechanism governs the time evolution: a quick approach to an almost stationary value is followed by a slow algebraic relaxation to the true stationary state.