Abstract
A grand canonical system of hard-core bosons in an optical lattice is considered. The bosons can occupy randomly N equivalent states at each lattice site. The limit N→∞ is solved exactly in terms of a saddle-point integration, representing a weakly-interacting Bose gas. In the limit N→∞ there is only a condensate if the fugacity of the Bose gas is larger than 1. Corrections in 1/N increase the total density of bosons but suppress the condensate. This indicates a depletion of the condensate due to increasing interaction at finite values of N.
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Ziegler, K. Interacting Bose Gas in an Optical Lattice. Journal of Low Temperature Physics 126, 1431–1443 (2002). https://doi.org/10.1023/A:1013860523104
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DOI: https://doi.org/10.1023/A:1013860523104