C^*-algebraic approach to the Bose-Hubbard model

Stefan Adams and Tony Dorlas

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Submission date: 03. Aug. 2007
Pages: 20
published in: Journal of mathematical physics, 48 (2007) 10, art-no. 103304 
DOI number (of the published article): 10.1063/1.2799349
Bibtex
MSC-Numbers: 82B10, 81R15, 82B26
PACS-Numbers: 05.30.-d, 05-30.ch, 05.30.Jp
Keywords and phrases: Bose-Hubbard model, long range hopping, pressure functional, relative entropy, relative Hamiltonian, large deviations
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Abstract:
We give a new derivation of the variational formula for the pressure of the long-range-hopping Bose-Hubbard model, which was first proved in [1]. The proof is analogous to that of a theorem on noncommutative large deviations introduced by Petz, Raggio and Verbeure [2] and could similarly be extended to more general Bose system of mean-field type. We apply this formalism to prove Bose-Einstein condensation for the case of small coupling.