Bose-Einstein condensation on hyperbolic spaces
Marius Lemm, Oliver Siebert
TL;DR
This paper proves Bose-Einstein condensation for the interacting Bose gas on hyperbolic spaces by linking it to the spectral gap of the Laplacian, providing a simplified proof in the infinite-volume limit.
Contribution
It offers a new proof of BEC on hyperbolic spaces based on spectral gap properties, extending understanding of quantum gases in curved geometries.
Findings
Bose-Einstein condensation occurs on hyperbolic spaces.
Spectral gap of the Laplacian is key to proving BEC.
Simplified proof method for BEC in curved spaces.
Abstract
A well-known conjecture in mathematical physics asserts that the interacting Bose gas exhibits Bose-Einstein condensation (BEC) in the thermodynamic limit. We consider the Bose gas on certain hyperbolic spaces. In this setting, one obtains a short proof of BEC in the infinite-volume limit from the existence of a volume-independent spectral gap of the Laplacian.
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Taxonomy
TopicsSpectral Theory in Mathematical Physics · Cold Atom Physics and Bose-Einstein Condensates · Stochastic processes and statistical mechanics