Spin Diffusion in Trapped Gases: Anisotropy in Dipole and Quadrupole Modes

TL;DR

This paper derives kinetic equations for trapped Bose gases with spin dependence, revealing anisotropic spin diffusion and non-conservation effects in dipole and quadrupole modes, advancing understanding of spin dynamics in quantum gases.

Contribution

It introduces a new kinetic framework including spin-dependent interactions and solves for diffusion constants, highlighting anisotropy and non-conservation phenomena in spin modes of trapped gases.

Findings

Unusual diffusion anisotropy in Bose gases in dipole and quadrupole modes.

Transverse and longitudinal collision times are identical in Fermi gases.

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

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 unusual diffusion anisotropy in both dipole and quadrupole modes. 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.