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arXiv:cond-mat/9608017

Functional Integration in Bose Systems with Hard-Core Interaction

K. Ziegler

Published Aug 5, 1996• 0 citations
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Abstract

A grand canonical ensemble of interacting bosons is considered. The zero temperature phase diagram is evaluated from the mean-field approximation of the functional integral. Three phases are found: a superfluid, a normal fluid and a Mott insulator.
DOI
10.48550/arxiv.cond-mat/9608017

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Several models of a strongly interacting Bose gas in an optical lattice are studied within the functionalintegral approach. The one-dimensional Bose gas is briefly discussed. Then the Bose-Einstein condensate and the Mott insulator of a three-dimensional Bose gas are described in mean-field approximation, and the corresponding phase diagrams are evaluated. Other characteristic quantities, like the spectrum of quasiparticle excitations and the static structure factor, are obtained from Gaussian fluctuations around the mean-field solutions. We discuss the role of quantum and thermal fluctuations, and determine the behavior of physical quantities in terms of density and temperature of the Bose gas. In particular, we study the dilute limit, where the mean-field equation becomes the Gross-Pitaevskii equation. This allows us to extend the Gross-