Renormalized expressions for the transport coefficients of a normal quantum fluid are derived from a nonlocal kinetic equation. As was shown in the classical case by Forster and Martin and by R\'esibois, the expressions for the transport coefficients separate naturally into "kinetic" and "direct" parts. The kinetic terms are proportional to matrix elements of the inverse of the kinetic kernel, and have the same general structure as the "bare" transport coefficients obtained from a local Boltzmann equation. The direct terms are proportional to matrix elements of the kernel itself, and have no counterpart in calculations based on a local kinetic equation, as in the kinetic theory of gases. We evaluate the transport coefficients using the weak-coupling approximation to the kernel derived in a previous paper. Results are given, first, for both Bose and Fermi fluids at arbitrary temperature, and then for the Fermi fluid near
T=0, where complete solutions are obtained. It is found that the direct parts of the shear viscosity and thermal conductivity are of higher order in
T than the kinetic parts, and are therefore negligible at very low temperature. The kinetic parts have the same leading temperature dependence as the predictions of the Landau theory. For the bulk viscosity, however, the direct and kinetic contributions begin at the same order (
T2) in the temperature.
Using kinetic theory, we calculate the shear viscosity and the spin-diffusion coefficient as well as the associated relaxation times for a two-component Fermi gas in two dimensions, as a function of temperature, coupling strength, polarization, and mass ratio of the two components. It is demonstrated that the minimum value of the viscosity decreases with the mass ratio, since Fermi blocking becomes less efficient. We furthermore analyze recent experimental results for the quadrupole mode of a two-dimensional gas in terms of viscous damping, obtaining a qualitative agreement using no fitting parameters.
We calculate expressions for the state-dependent quasiparticle lifetime ${\ensuremath{\tau}}_{\ensuremath{\sigma}}$, the thermal conductivity $\ensuremath{\kappa}$, the shear viscosity $\ensuremath{\eta}$, and discuss the spin diffusion coefficient
D for Fermi-liquid films in two dimensions. The expressions are valid for low temperatures and arbitrary polarization. In two dimensions, as in three dimensions, the integrals over the transition rates factor into energy and angular parts. However, the angular integrations contain a weak divergence. This problem is addressed using the method of K. Miyake and W. J. Mullin [Phys. Rev. Lett. 50, 197 (1983); J. Low Temp. Phys. 56, 499 (1984)]. The low-temperature expressions for the transport coefficients are essentially exact. We find that ${\ensuremath{\kappa}}^{\ensuremath{-}1}\ensuremath{\sim}TlnT$, and ${\ensuremath{\eta}}^{\ensuremath{-}1}\ensuremath{\sim}{T}^{2}$ for arbitrary polarizations $0\ensuremath{\le}\mathcal{P}\ensuremath{\le}1$. These results are in agreement with earlier zero-polarization results of H. H. Fu and C. Ebner [Phys. Rev. A 10, 338 (1974).], but differ from the temperature dependence of the shear viscosity found by D. S. Novikov (arXiv:cond-mat/0603184). They also differ from the discontinuous change of temperature dependence in
D from zero to nonzero polarization that was discovered by Miyake and Mullin. We note that in two dimensions the shear viscosity requires a unique analysis. We obtain predictions for the density, temperature, and polarization dependence of $\ensuremath{\kappa},\phantom{\rule{0.16em}{0ex}}\ensuremath{\eta}$, and
D for second-layer
3He films on graphite, and thin $^{3}\mathrm{He}\ensuremath{-}^{4}\mathrm{He}$ superfluid mixtures. For
3He on graphite, we find roughly an order of magnitude increase in magnitude for $\ensuremath{\kappa}$ and $\ensuremath{\eta}$ as the polarization is increased from 0 to 1. For
D a similar large increase is predicted from zero polarization to the polarization where
D is a maximum $(\ensuremath{\sim}0.74)$. We discuss the applicability of
3He thin films to the question of the existence of a universal lower bound for the ratio of the shear viscosity to the entropy density.
With neutron star applications in mind, we developed a theory of diffusion in mixtures of superfluid, strongly interacting Fermi liquids. By employing the Landau theory of Fermi liquids, we determined matrices that relate the currents of different particle species, their momentum densities, and the partial entropy currents to each other. Using these results, and applying the quasiclassical kinetic equation for the Bogoliubov excitations, we derived general expressions for the diffusion coefficients, which properly incorporate all the Fermi-liquid effects and depend on the momentum transfer rates between different particle species. The developed framework can be used as a starting point for systematic calculations of the diffusion coefficients (as well as other kinetic coefficients) in superfluid Fermi mixtures, particularly, in superfluid neutron stars.