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We formulate particle creation phenomena in Bose--Einstein condensates interms of conserving gapless mean field theory for weakly interacting Bosegases. The particle creation spectrum is calculated by rediagonalizing theBogoliubov--de Gennes (BdG) Hamiltonian in mean field theory. The conservationimplies that quasiparticle creation is accompanied by quantum backreaction tothe condensates. Particle creation in this mean field theory is found to beequivalent to that in quantum field theory (QFT) in curved spacetime. Anexpression is obtained for an effective metric affected by quantumbackreaction. The formula for the particle creation spectrum obtained in termsof QFT in curved spacetime is shown to be the same as that given byrediagonalizing the BdG Hamiltonian.

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