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

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 \cite{BD}. The proof is analogous to that of a theorem on noncommutative large deviations introduced by Petz, Raggio and Verbeure \cite{PRV} 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.