Role of fourth-order phase-space moments in collective modes of trapped Fermi gases

TL;DR

This paper investigates how including fourth-order phase-space moments in the Boltzmann equation improves the modeling of collective modes in ultracold Fermi gases, aligning theory more closely with experimental observations.

Contribution

It introduces a detailed method incorporating fourth-order moments into the Boltzmann equation for trapped Fermi gases, enhancing the accuracy of collective mode predictions.

Findings

Fourth-order moments improve agreement with experimental data.

Including fourth-order moments reduces collision effects at low temperatures.

The method better captures the transition from hydrodynamic to collisionless regimes.

Abstract

We study the transition from hydrodynamic to collisionless behavior in collective modes of ultracold trapped Fermi gases. To that end, we solve the Boltzmann equation for the trapped Fermi gas via the moments method. We showed previously that it is necessary to go beyond second-order moments if one wants to reproduce the results of a numerical solution of the Boltzmann equation. Here, we will give the detailed description of the method including fourth-order moments. We apply this method to the case of realistic parameters, and compare the results for the radial quadrupole and scissors modes at unitarity to experimental data obtained by the Innsbruck group. It turns out that the inclusion of fourth-order moments clearly improves the agreement with the experimental data. In particular, the fourth-order moments reduce the effect of collisions and therefore partially compensate the effect of the enhanced in-medium cross section at low temperatures.