Variational determination of multi-time Green's functions for degenerate bose systems and common pole structures of their hydrodynamic asymptotic behavior

Abstract

Variational determination of n-time (n=2,3,...) retarded Green's functions of Bose systems, whose equilibrium state is noninvariant under the group of gauge transformations, is given. Based on Bogoliubov's ideas of a reduced description of nonequilibrium states, the mathematical method of studying the hydrodynamic asymptotic behavior of Green's functions is developed and their pole structures are analyzed. It is shown that qualitatively new results for nonlinear interaction processes of the first-and second-sound waves in the superfluid Bose liquid are determined in terms of the three-time Green's functions, and that the increase in singularities in n-time (n≥4) Green's functions is caused by virtual effects only.