Phonon Dispersion in a Low-Temperature Weakly Interacting Bose Gas

Phonon dispersion in a weakly interacting Bose gas at low temperatures is investigated from a purely microscopic viewpoint. The role of the interaction and the effects of the condensate are emphasized in a generalized dielectric formulation. The leading terms for the frequency and damping rate of phonons are evaluated exactly from the zero of the dielectric constant. These terms may be viewed as the extension of Belyaev's zero-temperature results to low temperatures.