标题： 功能积分和束缚玻色气体的两点关联函数 显示英文标题

标题： The Functional Integration and the Two-Point Correlation Functions of the Trapped Bose Gas

摘要： 考虑了一个量子场论模型，该模型描述了在外部谐波势中的空间非均匀排斥玻色气体。 在泛函积分方法的框架内计算了玻色气体的两点热关联函数。 首先对“高能”泛函变量进行积分，然后对“低能”变量进行积分。 在单环近似下得到了低能变量的有效作用泛函。 通过平稳相位近似估计了关联函数的泛函积分表示。 在温度趋于零而由非均匀玻色气体占据的体积无限增大的极限情况下，展示了二维玻色气体关联函数的幂律渐进行为。 幂律行为由依赖于空间变量的临界指数控制。 显示英文摘要

摘要： A quantum field-theoretical model, which describes spatially non-homogeneous repulsive Bose gas in an external harmonic potential is considered. Two-point thermal correlation functions of the Bose gas are calculated in the framework of the functional integration approach. Successive integration over the ``high-energy'' functional variables first and then over the ``low-energy'' ones is used. The effective action functional for the low-energy variables is obtained in one loop approximation. The functional integral representations for the correlation functions are estimated by means of the stationary phase approximation. A power-law asymptotical behaviour of the correlators of the one-dimensional Bose gas is demonstrated in the limit, when the temperature is going to zero, while the volume occupied by the non-homogeneous Bose gas infinitely increases. The power-law behaviour is governed by the critical exponent dependent on the spatial arguments.