On Bose-Einstein condensation in the Luttinger-Sy model with finite interaction strength

TL;DR

This paper investigates Bose-Einstein condensation in a one-dimensional Luttinger-Sy model with finite repulsive interactions, demonstrating macroscopic occupation of the ground state above a critical density.

Contribution

It proves the occurrence of BEC in the Luttinger-Sy model with finite interaction strength, extending previous results to non-infinite interaction cases.

Findings

BEC occurs when particle density exceeds a temperature-dependent critical value

Ground state is macroscopically occupied in thermal equilibrium

Results apply to a model with randomly distributed impurities

Abstract

We study Bose-Einstein condensation (BEC) in the Luttinger-Sy model. Here, Bose point particles in one spatial dimension do not interact with each other, but, through a positive (repulsive) point potential with impurities which are randomly located along the real line according to the points of a Poisson process. Our emphasis is on the case in which the interaction strength is not infinite. As a main result, we prove that in thermal equilibrium the one-particle ground state is macroscopically occupied, provided that the particle density is larger than a critical one depending on the temperature.