Classification of equilibrium states and hydrodynamics of quantum Fermi-liquid mixtures with the vector order parameter

The classification of possible superfluid phases of the Fermi-liquids mixture is constructed. Thermodynamics is constructed and hydrodynamic equations of superfluid Fermi-liquid mixture with vector order parameter are derived. Thermodynamic values connected with spontaneous breaking of symmetry to phase transformations and spin rotations are presented in terms of the order parameter. A new entrainment effect connected with mutual influence of magnetic and orbital degrees of freedom is predicted. Spectra of collective excitations of the considered quantum Fermi-liquid mixture are obtained. Differences of this state from the states with scalar and tensor order parameters are considered. The cases of Galilean and relativistic invariance are considered.