Integrability breakdown in longitudinaly trapped, one-dimensional bosonic gases

TL;DR

This paper investigates how weak longitudinal trapping causes integrability breakdown in 1D bosonic gases, leading to relaxation mechanisms, but finds that in realistic experiments, this effect is negligible, preserving near-integrable dynamics.

Contribution

The study develops kinetic equations to analyze integrability breakdown due to finite collision delay times in trapped 1D bosonic gases, providing quantitative damping estimates.

Findings

Damping rate of monopole oscillations is negligible in experiments.

Longitudinal trapping does not significantly disrupt integrable dynamics.

Finite collision delay introduces a relaxation mechanism in 1D bosonic gases.

Abstract

A system of identical bosons with short-range (contact) interactions is studied. Their motion is confined to one dimension by a tight lateral trapping potential and, additionally, subject to a weak harmonic confinement in the longitudinal direction. Finite delay time associated with penetration of quantum particles through each other in the course of a pairwise one-dimensional collision in the presence of the longitudinal potential makes the system non-integrable and, hence, provides a mechanism for relaxation to thermal equilibrium. To analyse this effect quantitatively in the limit of a non-degenerate gas, we develop a system of kinetic equations and solve it for small-amplitude monopole oscillations of the gas. The obtained damping rate is long enough to be neglected in a realistic cold-atom experiment, and therefore longitudinal trapping does not hinder integrable dynamics of atomic gases in the 1D regime.