Transport in thin polarized Fermi-liquid films

We calculate expressions for the state-dependent quasiparticle lifetime, the thermal conductivity $\kappa$, the shear viscosity $\eta$, and discuss the spin diffusion coefficient $D$ for Fermi-liquid films in two dimensions. The expressions are valid for low temperatures and arbitrary polarization. The low-temperature expressions for the transport coefficients are essentially exact. We find that $\kappa^{-1} \sim T \ln{T}$, and $\eta^{-1} \sim T^{2}$ for arbitrary polarizations $0 \le {\mathcal{P}} \le 1$. We note that the shear viscosity requires a unique analysis. We utilize previously determined values for the density and polarization dependent Landau parameters to calculate the transition probabilities in the lowest order "$\ell = 0$ approximation," and thus we obtain predictions for the density, temperature and polarization dependence of the thermal conductivity, shear viscosity, and spin diffusion coefficient for thin \he3 films. Results are shown for second layer \he3 films on graphite, and thin \he3-\he4 superfluid mixtures. The density dependence is discussed in detail. For $\kappa$ and $\eta$ we find roughly an order of magnitude increase in magnitude from zero to full polarization. For $D$ a simialr large increase is predicted from zero polarization to the polarization where $D$ is a maximum ($\sim 0.74$). We discuss the applicability of \he3 thin films to the question of the existence of a universal lower bound for the ratio of the shear viscosity to the entropy density.