LINEAR DENSITY RESPONSE IN THE RANDOM-PHASE-APPROXIMATION FOR CONFINED BOSE VAPORS AT FINITE-TEMPERATURE

A linear response framework is set up for the evaluation of collective excitations in a confined vapour of interacting Bose atoms at finite temperature. Focusing on the currently relevant case of contact intera ctions between the atoms, the theory is developed within a random-phas e approximation with exchange. This approach is naturally introduced i n a two-fluid description by expressing the density response of both t he condensate and the non-condensate in terms of the response of a Har tree-Fock reference gas to the self-consistent Hartree-Fock potentials . Such an approximate account of correlations (i) preserves an interpl ay between the condensate and the non-condensate through off-diagonal components of the response, which instead vanish in the Hartree-Fock-B ogoliubov approximation;and (ii) yields a common resonant structure fo r the four partial response functions. The theory reduces to the tempe rature-dependent Hartree-Fock-Bogoliubov-Popov approximation for the f luctuations of the condensate when its coupling with the density fluct uations of the non-condensate is neglected. Analytic results are prese nted which are amenable to numerical calculations and to inclusion of damping rates.