An expression for the two-particle relaxation time of collective excitations on a distorted Fermi surface in the diffusion approach to kinetic theory is obtained. The general case of momentum-dependent diffusion and drift coefficients is considered. The temperature dependence of the obtained expression is established.
A consistent transformation from momentum space to energy space is performed for the diffusion equation within kinetic theory, with particle-number conservation explicitly preserved. Under the assumption of a constant single-particle level density, the equation reduces to a one-dimensional diffusion equation in energy space with consistent kinetic coefficients. The equivalence of the definitions of the equilibrium temperature in momentum space and in energy space is demonstrated. It is established that the inclusion of the energy dependence of the kinetic coefficients leads to an energy-dependent equilibrium temperature and a modification of the distribution function. The obtained results may be used to analyze relaxation processes in atomic nuclei and nonequilibrium dynamics of Fermi systems.
We compute the complete set of second-order transport coefficients of the unitary Fermi gas, a dilute gas of spin-1/2 particles interacting via an s-wave interaction tuned to infinite scattering length. The calculation is based on kinetic theory and the Chapman-Enskog method at second order in the Knudsen expansion. We take into account the exact two-body collision integral. We extend previous results on second-order coefficients related to shear stress by including terms related to heat flow and gradients of the fugacity. We confirm that the thermal relaxation time is given by the simple estimate ${\ensuremath{\tau}}_{\ensuremath{\kappa}}=\ensuremath{\kappa}m/({c}_{P}T)$ even if the full collision kernel is taken into account. Here, $\ensuremath{\kappa}$ is the thermal conductivity, m is the mass of the particles, cP is the specific heat at constant pressure, and T is the temperature.
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.