Derivation of the Landau quantum hydrodynamics for interacting bose systems

In this work we demonstrate that the basic equations of the Landau hydrodynamics may be derived directly from the quantum-mechanical microscopic N-body Hamiltonian, which is expressed as a functional of the local observables, namely, particle and current densities. The Landau quantum hydrodynamic equations are then the Heisenberg equations of motion of these quantities.