• DOI:10.1103/PhysRevB.53.9341
• Corpus ID: 2633647

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

@article{Griffin1996ConservingAG,
  title={Conserving and gapless approximations for an inhomogeneous Bose gas at finite temperatures.},
  author={Griffin},
  journal={Physical review. B, Condensed matter},
  year={1996},
  volume={53 14},
  pages={
          9341-9347
        }
}

• Griffin
• Published 7 February 1996
• Physics
• Physical review. B, Condensed matter

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.}