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arXiv · 2208.00103

Beyond mean field: condensate coupled with pair excitations

Stephen Sorokanich
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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 equations studied here are inspired by the work of Griffin, who derived this system in the study of finite temperature condensates. The techniques employed include a variational principle, which exploits the connection between unitary Bogoliubov rotations and a nonlinear operator equation for the pair excitation kernel. An iterative procedure for constructing solutions is also included.

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Stephen Sorokanich. 2022-07-29. Beyond mean field: condensate coupled with pair excitations. https://arxiv.org/abs/2208.00103

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