Molecular hydrodynamics of a weakly nonideal Bose gas. II. Green's functions for longitudinal fluctuations of particle and energy densities

General expressions are constructed for the two-time thermal Green's functions of the longitudinal fluctuations of the particle and energy densities in an interacting Bose system at a temperature above the critical value. The case of a weakly nonideal rarefied gas is considered in detail. The obtained expressions are of interpolation type. At wavelengths exceeding the mean-free path, they are identical to the expressions obtained in the hydrodynamic approximation, while in the limit of high frequencies and short wavelengths they reproduce the random phase approximation. Expressions are obtained for the transport coefficients in terms of the higher correlation functions that permit direct calculation of the coefficients of viscosity and thermal conductivity. At the same time, it is possible to obtain the results of Chapman–Enskog theory without recourse to solution of the Boltzmann equation.