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

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.

References in corpus (1)

• On the nature of Bose-Einstein condensation enhanced by localization

Cited by in corpus (4)

• On a condition for type-I Bose-Einstein condensation in random potentials in $d$ dimensions
• 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
• Thermodynamic limit of the Pieces' Model V2