Non-Conservation of Transverse Magnetization in Spin Diffusion in Trapped Boltzmann Gases

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. We find that the hydrodynamic diffusive modes cease to exist because interactions with different scattering lengths for up-up, up-down, and down-down spins lead to a spin-spin relaxation, that causes non-conservation of transverse magnetization. We give results for the quadrupole modes, the modes studied in experiments with equal scattering lengths. Instead of a linear dependence on relaxation time for the diffusive mode, we find a divergence at small . No such effect occurs in Fermi gases.