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

C. Malyshev·N. M. Bogoliubov
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Abstract

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.

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C. Malyshev, N. M. Bogoliubov. 2006-06-08. The Functional Integration and the Two-Point Correlation Functions of the Trapped Bose Gas. https://arxiv.org/abs/math-ph/0606026

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