Thermalisation of a trapped one-dimensional Bose gas via diffusion

TL;DR

This paper demonstrates how breaking integrability in a one-dimensional Bose gas leads to thermalisation through diffusive quasiparticle interactions, modeled by generalized hydrodynamics with diffusion, explaining slow thermalisation observed experimentally.

Contribution

It introduces a detailed hydrodynamic framework incorporating diffusion and force effects to describe thermalisation in non-integrable 1D Bose gases, supported by numerical simulations.

Findings

Diffusive quasiparticle interactions drive thermalisation.

Generalized hydrodynamics with diffusion accurately models the process.

Slow thermalisation rates are due to modes with small diffusion coefficients.

Abstract

For a decade the fate of a one-dimensional gas of interacting bosons in an external trapping potential remained mysterious. We here show that whenever the underlying integrability of the gas is broken by the presence of the external potential, the inevitable diffusive rearrangements between the quasiparticles, quantified by the diffusion constants of the gas, eventually lead the system to thermalise at late times. We show that the full thermalising dynamics can be described by the generalised hydrodynamics with diffusion and force terms, and we compare these predictions with numerical simulations. Finally, we provide an explanation for the slow thermalisation rates observed in numerical and experimental settings: the hydrodynamics of integrable models is characterised by a continuity of modes, which can have arbitrarily small diffusion coefficients. As a consequence, the approach to thermalisation can display pre-thermal plateau and relaxation dynamics with long polynomial finite-time corrections.