We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.
MiS Preprint
71/2007
C$^*$-algebraic approach to the Bose-Hubbard model
Stefan Adams and Tony Dorlas
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.
