Diffusion in superfluid Fermi mixtures: General formalism

TL;DR

This paper develops a comprehensive theoretical framework for diffusion in superfluid, strongly interacting Fermi mixtures, with applications to neutron star physics, by combining Landau Fermi liquid theory and kinetic equations for Bogoliubov excitations.

Contribution

It introduces a general formalism for calculating diffusion coefficients in superfluid Fermi mixtures, incorporating Fermi liquid effects and inter-species momentum transfer.

Findings

Derived general expressions for diffusion coefficients.

Established relations between particle currents and momentum densities.

Framework applicable to superfluid neutron star matter.

Abstract

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.