Generalized Bose-Einstein Condensation in the Kac-Luttinger Model

Abstract

In this article, we prove generalized Bose–Einstein condensation (BEC) at zero temperature in the random Kac–Luttinger model for repulsive two-particle interactions that are scaled suitably in the limit of large volume. Compared to previous works, by proving generalized condensation rather than the macroscopic occupation of finitely many single-particle states (type-I BEC), we can allow for stronger two-particle interactions. We discuss implications of the result which include a possible transition in the type of the condensation.