A microscopic theory for deriving hydrodynamic equations for Fermi superfluids is developed and applied to the two-fluid hydrodynamic equations in superfluid 3He-B near the transition temperature. It is shown how the two-fluid hydrodynamic equations as well as the Boltzmann-type transport equations for the Bogoliubov-Valatin quasiparticles are derived from the matrix kinetic equation. Special attention is paid to the derivation of the particle number conservation law and also to the definition of the chemical potential when the system deviates from local equilibrium.
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Hara, J., Nagai, K. Microscopic derivation of the hydrodynamic equations for the superfluid Fermi system: Application to the two-fluid hydrodynamic equations in superfluid 3He-B. J Low Temp Phys 34, 351–383 (1979). https://doi.org/10.1007/BF00117157
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DOI: https://doi.org/10.1007/BF00117157