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Phase transitions in three-dimensional bosonic systems in optical lattices

H KleinertInstitut für Theoretische Physik, Freie Universität Berlin, Arnimallee 14, D-14195 Berlin, GermanyZ NarzikulovInstitute of Nuclear Physics, Tashkent 100214, UzbekistanAbdulla RakhimovInstitut für Theoretische Physik, Freie Universität Berlin, Arnimallee 14, D-14195 Berlin, Germany
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We formulate the Collective Quantum Field Theory for three-dimensional bosonic optical lattices and evaluate its consequences in a mean-field approximation to two collective fields, proposed by Fred Cooper et al. and in a lowest-order Variational Perturbation Theory (VPT). It is shown that present mean-field approximation predicts some essential features of the experimentally observed dependence of the critical temperature on the coupling strength and a second - order quantum phase transition.In contrast to a recent prediction for atomic gases by Fred Cooper et. al., we find no superfluid state with zero condensate fraction.

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