Beyond mean-field: Condensate coupled with pair excitations

Abstract

We prove existence results for a system of partial differential equations describing the approximate condensate wavefunction and pair-excitation kernel of a dilute T = 0 Bose gas in the stationary setting, in the presence of a trapping potential and repulsive pairwise atomic interactions. Notably, the Hartree-type equation for the condensate in this system contains contributions from non-condensate particles, and the pair excitation kernel satisfies a nonlinear operator equation. The techniques employed include a direct variational principle and also an iterative procedure for constructing solutions.