Conserving and gapless approximations for an inhomogeneous Bose gas at finite temperatures

Journal Article · Mon Apr 01 04:00:00 EST 1996 · Physical Review, B: Condensed Matter

DOI:https://doi.org/10.1103/PhysRevB.53.9341· OSTI ID:280195

Griffin, A ^[1]

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1. Department of Physics, University of Toronto, Toronto, Ontario, M5S1A7 (CANADA)

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{close_quote}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. {copyright} {ital 1996 The American Physical Society.}

• OSTI ID: 280195
• Journal Information: Physical Review, B: Condensed Matter, Journal Name: Physical Review, B: Condensed Matter Journal Issue: 14 Vol. 53; ISSN PRBMDO; ISSN 0163-1829
• Country of Publication: United States
• Language: English

Related Subjects

66 PHYSICS
BOSE-EINSTEIN CONDENSATION
CONSERVATION LAWS
EQUATIONS OF MOTION
EXCITATION FUNCTIONS
EXCITED STATES
HARTREE-FOCK-BOGOLYUBOV THEORY
RESPONSE FUNCTIONS
SPECTRA