Beyond mean-field properties of binary dipolar Bose mixtures at low temperatures

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We rigorously analyze the low-temperature properties of homogeneous three-dimensional two-component Bose mixture with dipole-dipole interaction. For such a system the effective hydrodynamic action that governs the behavior of low-energy excitations is derived. The infrared structure of the exact single-particle Green's functions is obtained in terms of macroscopic parameters, namely the inverse compressibility and the superfluid density matrices. Within one-loop approximation we calculate the anisotropic superfluid and condensate densities and give the beyond mean-field stability condition for the binary dipolar Bose gas. A brief variational derivation of the coupled equations that describe macroscopic hydrodynamics of the system in the external non-uniform potential at zero temperature is presented.