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Bose-Einstein Condensation in the Luttinger-Sy Model

Olivier Lenoble·Valentin Zagrebnov
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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.

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Olivier Lenoble, Valentin Zagrebnov. 2006-04-27. Bose-Einstein Condensation in the Luttinger-Sy Model. https://arxiv.org/abs/math-ph/0604068

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