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

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dc.creatorMalyshev, C.
dc.creatorBogoliubov, N. M.
dc.date2006-06-08
dc.date.accessioned2026-07-07T07:16:55Z
dc.date.available2026-07-07T07:16:55Z
dc.descriptionA 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.
dc.descriptionExtended version of the talk at The 8th International Conference ``Path Integrals from Quantum Information to Cosmology'' (Prague, June 6-10, 2005)
dc.identifierhttps://arxiv.org/abs/math-ph/0606026
dc.identifierhttp://arxiv.org/abs/math-ph/0606026
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/113762
dc.subjectMathematical Physics
dc.subjectStatistical Mechanics
dc.subjectExactly Solvable and Integrable Systems
dc.subject81S40; 42C10
dc.titleThe Functional Integration and the Two-Point Correlation Functions of the Trapped Bose Gas
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