Crossover from collisionless to collisional spin dynamics of polarized fermions

TL;DR

This paper investigates how polarized fermions transition from collisionless spin wave oscillations to collisional spin diffusion in high-temperature trapped gases, using a quantum Boltzmann equation to analyze the crossover.

Contribution

It provides a detailed theoretical analysis of the crossover from collisionless to collisional spin dynamics, including analytical solutions and numerical validation.

Findings

Dispersive spin wave oscillations in the collisionless regime

Diffusive spin dynamics in the collisional regime

Analytical solutions match numerical results in both regimes

Abstract

We study the transverse spin dynamics of trapped polarized Fermi gases in the high temperature limit. In the non-interacting collisionless regime, a magnetic field gradient induces collective spin wave oscillations. In the strongly interacting collisional regime, the dynamics are governed by spin diffusion. These two limits have been extensively studied both experimentally and theoretically, but the crossover between them has received less attention. In this paper, we use a quantum Boltzmann equation to study transverse spin dynamics and show how the excitations evolve from dispersive to diffusive in the high temperature limit. We provide analytical solutions in the two limiting regimes, which agree well with our numerical results.