Linear density response in the random phase approximation for confined Bose vapours at finite temperature

TL;DR

This paper develops a linear response theory within the random phase approximation for confined Bose vapours at finite temperature, capturing collective excitations and correlations between condensate and non-condensate components.

Contribution

It introduces a two-fluid response framework that includes exchange effects and preserves condensate-non-condensate interplay, extending beyond Hartree-Fock-Bogolubov approximations.

Findings

Provides analytic expressions for density response functions.

Framework accommodates damping rates and finite temperature effects.

Recovers known approximations in specific limits.

Abstract

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 interactions between the atoms, the theory is developed within a random phase approximation with exchange. This approach is naturally introduced in a two-fluid description by expressing the density response of both the condensate and the non-condensate in terms of the response of a Hartree-Fock reference gas to the selfconsistent Hartree-Fock potentials. Such an approximate account of correlations (i) preserves an interplay between the condensate and the non-condensate through off-diagonal components of the response, which instead vanish in the Hartree-Fock-Bogolubov approximation; and (ii) yields a common resonant structure for the four partial response functions. The theory reduces to the temperature-dependent Hartree-Fock-Bogolubov-Popov approximation for the fluctuations of the condensate when its coupling with the density fluctuations of the non-condensate is neglected. Analytic results are presented which are amenable to numerical calculations and to inclusion of damping rates.