Bose-Einstein Condensation in the Luttinger-Sy Model

Abstract

We present a rigorous study of the Bose-Einstein condensation in the Luttinger-Sy model. We prove the existence of the condensation in this one-dimensional model of the perfect boson gas placed in the Poisson random potential of singular point impurities. To tackle the off-diagonal long-range order we calculate explicitly the corresponding space-averaged one-body reduced density matrix. We show that mathematical mechanism of the Bose-Einstein condensation in this random model is similar to condensation in a one-dimensional nonrandom hierarchical model of scaled intervals. For the Luttinger-Sy model we prove the Kac-Luttinger conjecture, i.e., that this model manifests a type I BEC localized in a single "largest" interval of logarithmic size.

References in corpus (2)

• Bose-Einstein condensation and superfluidity of dilute Bose gas in a random potential
• Condensation in a Disordered Infinite-Range Hopping Bose-Hubbard Model

Cited by in corpus (4)

• Decay of correlations and absence of superfluidity in the disordered Tonks-Girardeau gas
• Condensation in a Disordered Infinite-Range Hopping Bose-Hubbard Model
• On the effect of repulsive interactions on Bose-Einstein condensation in the Luttinger-Sy model
• On Bose-Einstein condensation in interacting Bose gases in the Kac-Luttinger model