Spin Diffusion in a Two-Dimensional Degenerate Fermi Liquid

The spin-diffusion coefficient $D$ of a polarized two-dimensional degenerate Fermi fluid is evaluated as a model of adsorbed ${}_{}{}^3{}_{}{}^{}\mathrm{He}$. Because in two dimensions, for zero or weak polarization, the only allowed scattering angles are 0 and $\pi$, the transport coefficients become expressible in terms of Landau parameters without approximation. For unpolarized and weakly polarized systems it is shown that $D^{-1\mathrm{}}\sim T^2\ln T$ and $T^2\ln \left(\mathrm{polarization}\right)$, respectively. The two-dimensional kinetic equation is found to be exactly solvable.