Kinetic equation for dilute, spin-polarized quantum systems

Abstract

A kinetic equation, which includes the effects of degeneracy, is derived for dilute, polarized systems by the Green's function method of Kadanoff and Baym. When the Born approximation is used for the self-energy, the equation reduces to a result due to Silin. In the Boltzmann limit our result is equivalent to the equation of Lhuillier and Laloë, with the addition of a mean-field drift term analogous to that appearing in the Landau-Silin equation. Our kinetic equation is used to derive an expression for the transverse spin-diffusion relaxation time, τ〉, for a Fermi system. In the Boltzmann and low-polarization limits τ〉 reduces to τ ∥, the longitudinal relaxation time. However, in a highly polarized degenerate system τ〉 can be very much shorter than τ ∥.