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