On a condition for type-I Bose-Einstein condensation in random potentials in $d$ dimensions

Abstract

In this paper we discuss Bose-Einstein condensation (BEC) in systems of pairwise non-interacting bosons in random potentials in $d$ dimensions. Working in a rather general framework, we provide a "gap condition" which is sufficient to conclude existence of type-I BEC in probability and in the $r$th mean. We illustrate our results in the context of the well-known (one-dimensional) Luttinger-Sy model. Here, whenever the particle density exceeds a critical value, we show in addition that only the ground state is macroscopically occupied.

arXiv comment26 pages

References in corpus (4)

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Cited by in corpus (5)

• On the effect of repulsive interactions on Bose-Einstein condensation in the Luttinger-Sy model
• On the spectral gap in the Kac-Luttinger model and Bose-Einstein condensation
• On the spectral gap of one-dimensional Schrödinger operators on large intervals
• On Bose-Einstein condensation in interacting Bose gases in the Kac-Luttinger model
• Off-diagonal long-range order for the free Bose gas via the Feynman--Kac formula