Particle creation in Bose-Einstein condensates: Theoretical formulation based on conserving gapless mean-field theory

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.