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MiS Preprint

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

Stefan Adams and Tony Dorlas


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.

Aug 3, 2007
Aug 3, 2007
MSC Codes:
82B10, 81R15, 82B26
05.30.-d,, 05.30.Jp
Bose-Hubbard model, long range hopping, pressure functional, relative entropy, relative Hamiltonian, large deviations

Related publications

2007 Repository Open Access
Stefan Adams and Wolfgang König

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

In: Journal of mathematical physics, 48 (2007) 10, p. 103304