Higher Orders of Perturbation Theory in Nonlocal Hydrodynamics of a Quantum Many-Particle System

Abstract

In [1–5] it is demonstrated that the problem of the statistical quantum mechanics of a many-particle system in the linear approximation of weak hydrodynamic perturbations is equivalent to a hydrodynamic problem. The material relations for the corresponding hydrodynamic model are nonlocal in space and time. In the present paper, this approach is generalized to the nonlinear case. A recursion procedure for computing higher-order nonlinear terms in the material relations is constructed.