Identifying diffusive length scales in one-dimensional Bose gases

TL;DR

This paper investigates the role of diffusion in one-dimensional Bose gases, revealing it is significant mainly at high wavelengths, while relaxation is primarily due to ballistic dephasing linked to phonon lifetimes.

Contribution

It provides a quantitative analysis of diffusive effects in 1D Bose gases and clarifies the dominant relaxation mechanisms across different regimes.

Findings

Diffusion is relevant only for high wavelength excitations.

Ballistic dephasing dominates relaxation in most regimes.

Phonon lifetime relates to the dephasing timescale.

Abstract

In the hydrodynamics of integrable models, diffusion is a subleading correction to ballistic propagation. Here we quantify the diffusive contribution for one-dimensional Bose gases and find it most influential in the crossover between the main thermodynamic regimes of the gas. Analysing the experimentally measured dynamics of a single density mode, we find diffusion to be relevant only for high wavelength excitations. Instead, the observed relaxation is solely caused by a ballistically driven dephasing process, whose time scale is related to the phonon lifetime of the system and is thus useful to evaluate the applicability of the phonon bases typically used in quantum field simulators.