Conserving and gapless approximations for an inhomogeneous Bose gas at finite temperatures
- 1 April 1996
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review B
- Vol. 53 (14), 9341-9347
- https://doi.org/10.1103/physrevb.53.9341
Abstract
We derive and discuss the equations of motion for the condensate and its fluctuations for a dilute, weakly interacting Bose gas in an external potential within the self-consistent Hartree-Fock-Bogoliubov (HFB) approximation. Account is taken of the depletion of the condensate and the anomalous Bose correlations, which are important at finite temperatures. We give a critical analysis of the self-consistent HFB approximation in terms of the Hohenberg-Martin classification of approximations (conserving vs gapless) and point out that the Popov approximation to the full HFB gives a gapless single-particle spectrum at all temperatures. The Beliaev second-order approximation is discussed as the spectrum generated by functional differentiation of the HFB single-particle Green's function. We emphasize that the problem of determining the excitation spectrum of a Bose-condensed gas (homogeneous or inhomogeneous) is difficult because of the need to satisfy several different constraints.This publication has 15 references indexed in Scilit:
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