Numerical solution of the Boltzmann equation for trapped Fermi gases with in-medium effects

TL;DR

This paper presents a numerical method to solve the Boltzmann equation for trapped Fermi gases, incorporating in-medium effects, and demonstrates its effectiveness through realistic simulations that align well with experimental data.

Contribution

The study introduces a numerical approach that includes mean-field and in-medium cross-section modifications for Fermi gases, improving the modeling of their dynamics.

Findings

In-medium effects increase collision rates significantly.

The method accurately reproduces anisotropic expansion and quadrupole mode oscillations.

In-medium effects have moderate impact on collective mode properties.

Abstract

Using the test-particle method, we solve numerically the Boltzmann equation for an ultra-cold gas of trapped fermions with realistic particle number and trap geometry in the normal phase. We include a mean-field potential and in-medium modifications of the cross-section obtained within a T matrix formalism. After some tests showing the reliability of our procedure, we apply the method to realistic cases of practical interest, namely the anisotropic expansion of the cloud and the radial quadrupole mode oscillation. Our results are in good agreement with experimental data. Although the in-medium effects significantly increase the collision rate, we find that they have only a moderate effect on the anisotropic expansion and on frequency and damping rate of the quadrupole mode.