Research of quantum statistical mechanics in terms of random fields

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Various physically interesting systems of boson gas are investigated by means of the Random(Point) Fields.For a model of a mean-field interacting boson gas trapped by a weak harmonic potential, it is shown that in the Weak Harmonic Trap limit there are two phases which are different from each other in the local density : finite in one phase and divergent in another phase. The mechanism of the divergence is considered in the different scale using random field, which makes the role of BEC clear.For the perfect Bose-gas trapped in extremely anisotropic boxes, quasi BEC states as well as usual BEC occur. We investigated particle distribution in these cases.Limit theorems on the particle distribution, including the large deviation principle, are also established for the ideal boson gas in BEC.