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.
Transport coefficients of superfluid dipolar Fermi gas are calculated by using the Boltzmann equation approach. The interaction between Bogoliubov-Bogoliubov quasiparticles in the collision integral is considered in binary process. The shear viscosities nxz↑ = nyy↑,nxy↑; nxz↑ ≈ nyz↑; and nu↑ are proportional to T-6; T-8; and T-10 , respectively. Also, we have found the elements of the diffusive thermal conductivities Kxx↑= Kyy↑ with temperature dependency T-5 and Ku↑ which is proportional to T-7 and other components which are zero.
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.
In interaction-dominated two-dimensional electron gases at intermediate temperatures, electron transport is not diffusive as in the conventional Drude picture but instead hydrodynamic. The relevant transport coefficient in this regime is the shear viscosity. Here, we develop a numerically exact basis expansion to solve the Fermi liquid equation, and apply it to compute the shear viscosity of the electron gas with screened Coulomb interactions. Our calculations are valid at all temperatures and in particular describe the response beyond the asymptotic low-temperature limit, where perturbative approaches exist. We show that even in this low-temperature limit, there is a nonanalytic exchange contribution to the shear viscosity, highlighting the need for a full nonperturbative solution of the Fermi liquid equation. We hope that the techniques developed in this work will serve as a platform to determine the response of interacting Fermi liquids.