Hydrodynamics of a Multi-Component Bosonic Superfluid

We obtain the superfluid hydrodynamic equations of a multi-component Bose gas with short-ranged interac-tions at zero temperature under the local equilibrium assumption and show that the quantum pressure is generally present in the nonuniform case.Our approach can be extended to systems with long-range interactions such as dipole-dipole interactions by treating the Hartree energy properly.For a highly symmetric superfluid,we obtain the excitation spectrum and show that except for the density phonon,all other excitations are all degenerate.The implication of our results is discussed.