Bose--Einstein condensation of the gapless Hartree--Fock model Hamiltonian

Ahmed S. Hassan, Azza M. El-Badry, Shemi S.M. Soliman

Ze Cheng

Tama Khellil, Axel Pelster

Nick P. Proukakis, S. A. Morgan, Seok Jin Choi +1 more

We present two gapless mean-field theories for trapped Bose-Einstein condensates, and compare them to the better known Hartree-Fock-Bogoliubov (HFB)-Popov approach. The proposed theories are based on suitable inclusion of the simplest anomalous average of the Bose field operator. This leads to an effective interaction between two atoms which is both temperature and density dependent, as opposed to the HFB-Popov approach, for which it is constant. These theories are compared to the HFB-Popov approach for a trapped one-dimensional condensate of 2000 atoms. The density profiles and excitation frequencies of the proposed theories differ from the corresponding HFB-Popov ones by at most a few percent.

Vyacheslav I. Yukalov, Hagen M. Kleinert

A dilute Bose system with Bose-Einstein condensate is considered. It is shown that the Hartree-Fock-Bogoliubov approximation can be made both conserving as well as gapless. This is achieved by taking into account all physical normalization conditions, that is, the normalization condition for the condensed particles and that for the total number of particles. Two Lagrange multipliers, introduced for preserving these normalization conditions, make the consideration completely self-consistent.

David A. W. Hutchinson, Karen G. Burnett, Kenneth M. Dodd +7 more