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.
- Publication:
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arXiv e-prints
- Pub Date:
- November 2019
- DOI:
- 10.48550/arXiv.1911.03200
- arXiv:
- arXiv:1911.03200
- Bibcode:
- 2019arXiv191103200K
- Keywords:
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- Mathematical Physics;
- Quantum Physics
- E-Print:
- 26 pages