

Preprint 71/2007
C*-algebraic approach to the Bose-Hubbard model
Stefan Adams and Tony Dorlas
Contact the author: Please use for correspondence this email.
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
Download full preprint: PDF (226 kB), PS ziped (260 kB)
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.