Transverse Spin Diffusion in a Dilute Spin-Polarized Degenerate Fermi Gas

TL;DR

This paper provides an exact calculation of the transverse spin-diffusion coefficient in a dilute, spin-polarized Fermi gas with s-wave scattering, revealing a novel intermediate regime between high and low field behaviors.

Contribution

It introduces an exact solution for the spin diffusion coefficient dependence on temperature and field, and analyzes the failure of Fermi-liquid phase space arguments for spin-flip processes.

Findings

Identification of an intermediate regime with distinct diffusion behavior

Explicit temperature and field dependence of the diffusion coefficients

Evidence supporting the intermediate regime in helium mixture experiments

Abstract

We re-examine the calculation of the transverse spin-diffusion coefficient in a dilute degenerate spin-polarized Fermi gas, for the case of s-wave scattering. The special feature of this limit is that the dependence of the spin diffusion coefficient on temperature and field can be calculated explicitly with no further approximations. This exact solution uncovers a novel intermediate behavior between the high field spin-rotation dominated regime in which $D_{\bot} \propto H^{-2}$, $D_{\parallel} \propto T^{-2}$, and the low-field isotropic, collision dominated regime with $D_{\bot} = D_{\parallel} \propto T^{-2}$. In this intermediate regime, $D_{\bot ,\parallel} \propto T^{-2}$ but $D_{\bot} \neq D_{\parallel}$. We also present an analytical calculation of the self-energy in the s-wave approximation for a dilute spin-polarized Fermi gas, at zero temperature. This emphasizes the failure of the conventional Fermi-liquid phase space arguments for processes involving spin flips. We close by reviewing the evidence for the existence of the intermediate regime in experiments on weakly spin-polarized $^3{\rm He}$ and $^3{\rm He} - ^4{\rm He}$ mixtures.