Research of quantum statistical mechanics in terms of random fields

利用无规（点）场方法研究了各种有趣的玻色子气体系统.对于一个被弱谐振势囚禁的平均场相互作用玻色子气体模型，证明了在弱谐振势阱极限下存在两个局域密度不同的相：一个相是有限的，另一个相是发散的.利用无规场在不同尺度下考虑了发散的机制，使BEC的作用更加清晰，对于囚禁在极端各向异性盒中的理想玻色气体，不仅可以产生通常的BEC态，而且可以产生准BEC态.我们研究了这些情况下的粒子分布，并建立了BEC中理想玻色子气体粒子分布的极限定理，包括大偏差原理。

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.