Transport equations and linear response of superfluid Fermi mixtures in neutron stars

We study transport properties of a strongly interacting superfluid mixture of two Fermi-liquids. A typical example of such matter is the neutron-proton liquid in the cores of neutron stars. To describe the mixture, we employ the Landau theory of Fermi-liquids, generalized to allow for the effects of superfluidity. We formulate the kinetic equation and analyze linear response of the system to vector (e.g., electromagnetic) perturbation. In particular, we calculate the transverse and longitudinal polarization functions for both liquid components. We demonstrate, that they can be expressed through the Landau parameters of the mixture and polarization functions of noninteracting matter (when the Landau quasiparticle interaction is neglected). Our results can be used, e.g., for studies of the kinetic coefficients and low-frequency long-wavelength collective modes in superfluid Fermi-mixtures.