Using the methods of kinetic theory, expressions for the diffusion and drift coefficients for a cold Fermi system are obtained. Their dependencies on the momentum are calculated for the step distribution function as well as in the case of excitation of a particle-hole pair.
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.
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.
The set of equations for the two-particle Green's functions in a nonequilibrium medium is derived in the diffusive approximation. Both the two- and single-particle Green's functions are calculated when matter is in the ground state. It is shown that the Landau Fermi-liquid consideration is correct when the interaction between particles in matter is rather weak or when matter is not too dense. In the opposite cases the energy spectrum of the particles is rearranged so that the step in the momentum distribution of the particles disappears. The applicability of the Landau Fermi-liquid theory is established in the general case.