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Hartree-Fock-Bogoliubov theory of a charged Bose gas at finite temperature

B. Davoudi·A. Minguzzi·M. P. Tosi
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Abstract

We critically examine the Hartree-Fock-Bogoliubov (HFB) solution of the equations of motion for condensate fluctuations in a weakly coupled plasma of charged bosons at finite temperature. Analytic expressions are derived for the first two infrared-divergent terms in both the momentum distribution of the noncondensate and the anomalous Bose correlation function at low momenta. Incorporation into the theory of the appropriate form of the Hugenholtz-Pines relation for the chemical potential is needed to cancel an unphysical divergence. Exact cancellation of infrared-divergent terms is demonstrated in the HFB shift of the single-particle excitation energy away from the Bogoliubov value at long wavelengths, with the residual terms raising it towards the plasma frequency at low temperature. Numerical illustrations are presented for a number of properties of the boson plasma as functions of temperature and density in the weak-coupling regime: these are the chemical potential, the condensate fraction, the normal and anomalous momentum distribution functions and the corresponding one-body density matrices, and the dispersion relation of single-particle excitations.

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B. Davoudi, A. Minguzzi, M. P. Tosi. 2002-01-23. Hartree-Fock-Bogoliubov theory of a charged Bose gas at finite temperature. https://doi.org/10.1103/physrevb.65.144507

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