Boltzmann equation with double-well potentials

TL;DR

This paper investigates the dynamics of classical gases in double-well potentials using the Boltzmann equation, providing numerical and analytical insights into relaxation times and extending findings to fermionic mixtures relevant for cold atom experiments.

Contribution

It introduces a simple analytical model for relaxation times and applies it to classical and fermionic gases in double-well traps, combining numerical and theoretical approaches.

Findings

Analytical estimates of relaxation times match numerical results.

Numerical simulations of gas dynamics in double-well potentials.

Predictions for fermionic mixtures in experimental cold atom setups.

Abstract

We study the dynamics of an interacting classical gas trapped in a double-well potential at finite temperature. Two model potentials are considered: a cubic box with a square barrier in the middle, and a harmonic trap with a gaussian barrier along one direction. The study is performed using the Boltzmann equation, solved numerically via the test-particle method. We introduce and discuss a simple analytical model that allows to provide estimates of the relaxation time, which are compared with numerical results. Finally, we use our findings to make numerical and analytical predictions for the case of a fermionic mixture in the normal-fluid phase in a realistic double-well potential relevant for experiments with cold atoms.