The Bogoliubov theory of bose condensation as a mean field theory

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.

P. G. Kevrekidis, D. J. Frantzeskakis, R. Carretero-González

Yasunari Kurita, Michikazu Kobayashi, Hideki Ishihara +1 more

We formulate particle-creation phenomena in Bose-Einstein condensates in terms of conserving gapless mean-field theory for weakly interacting Bose gases. The particle-creation spectrum is calculated by rediagonalizing the Bogoliubov--de Gennes (BdG) Hamiltonian in mean-field theory. The conservation implies that quasiparticle creation is accompanied by quantum back reaction to the condensates. Particle creation in this mean-field theory is found to be equivalent to that in quantum field theory (QFT) in curved space-time. An expression is obtained for an effective metric affected by quantum back reaction. The formula for the particle-creation spectrum obtained in terms of QFT in curved space-time is shown to be the same as that given by rediagonalizing the BdG Hamiltonian.

Takafumi Kita

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

E. J. V. de Passos

I formulate a mean-field theory of Bose-Einstein condensation based on number-conserving many-body theory. I use techniques commonly adopted in nuclear structure theories to derive the mean-field equations. I compare my formulation with the Bogoliubov approach and I emphasize the key role played by the zero-energy eigenmode when we contrast these two approaches. The differences with analogous previous formulation are also pointed out.