On Bose-Einstein condensation in interacting Bose gases in the Kac-Luttinger model

Abstract

We study interacting Bose gases of dimensions $2\le d\in \mathbb{N}$ at zero temperature in a random model known as the Kac-Luttinger model. Choosing the pair-interaction between the bosons to be of a mean-field type, we prove (complete) Bose-Einstein condensation in probability or with probability almost one into the minimizer of a Hartree-type functional. We accomplish this by building upon very recent results by Alain-Sol Sznitman on the spectral gap of the noninteracting Bose gas.

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