Numerical solution of the Boltzmann equation for the collective modes of trapped Fermi gases

TL;DR

This paper presents a numerical approach to solving the Boltzmann equation for trapped Fermi gases, focusing on collective modes, and compares results with traditional moment methods to improve accuracy.

Contribution

The authors introduce a test-particle numerical method for solving the Boltzmann equation and demonstrate its effectiveness in modeling collective modes in trapped Fermi gases, improving upon moment-based approaches.

Findings

Numerical results show similar response shapes to moment methods.

Relaxation times from simulations are longer than moment predictions.

Including fourth-order moments aligns moment method results with simulations.

Abstract

We numerically solve the Boltzmann equation for trapped fermions in the normal phase using the test-particle method. After discussing a couple of tests in order to estimate the reliability of the method, we apply it to the description of collective modes in a spherical harmonic trap. The numerical results are compared with those obtained previously by taking moments of the Boltzmann equation. We find that the general shape of the response function is very similar in both methods, but the relaxation time obtained from the simulation is significantly longer than that predicted by the method of moments. It is shown that the result of the method of moments can be corrected by including fourth-order moments in addition to the usual second-order ones and that this method agrees very well with our numerical simulations.