Quantum hydrodynamics and two-fluid dynamics

It is shown how two fluid dynamical equations for superfluid He4 are derived from quantum hydrodynamical Hamiltonian, represented in terms of the quantized canonical conjugate variables, mass density rho(x) and velocity field v(x). An essential assumption is that expectation value of v(x) should be identified with the superfluid velocity. The random phase approximation is applied to higher order dynamical correlation function of rho and v appearing in the equations of motion. This approximation implies to decouple the correlation into the hydrodynamical degrees of freedom and the incoherent one of thermal phonon. It is found that a set of equations thus obtained is consistent with the two fluid dynamical one, having been widely used in the phenomenological theories. (auth.)