Anisotropic Spin Diffusion in Trapped Boltzmann Gases

TL;DR

This paper derives kinetic equations for trapped Bose gases with spin dependence, revealing anisotropic spin diffusion and non-conservation of transverse spin, which affect hydrodynamic modes.

Contribution

It introduces a detailed kinetic theory including spin-dependent interactions and solves for spin-wave properties in trapped Bose gases.

Findings

Bose gases exhibit anisotropic spin diffusion unlike Fermi gases.

Lack of spin isotropy causes non-conservation of transverse spin.

Novel effects on hydrodynamic modes due to spin non-conservation.

Abstract

Recent experiments in a mixture of two hyperfine states of trapped Bose gases show behavior analogous to a spin-1/2 system, including transverse spin waves and other familiar Leggett-Rice-type effects. We have derived the kinetic equations applicable to these systems, including the spin dependence of interparticle interactions in the collision integral, and have solved for spin-wave frequencies and longitudinal and transverse diffusion constants in the Boltzmann limit. We find that, while the transverse and longitudinal collision times for trapped Fermi gases are identical, the Bose gas shows diffusion anisotropy. Moreover, the lack of spin isotropy in the interactions leads to the non-conservation of transverse spin, which in turn has novel effects on the hydrodynamic modes.