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Finite-temperature correlations in the trapped Bose gas

N. M. Bogoliubov·R. K. Bullough·V. S. Kapitonov·C. Malyshev·J. Timonen
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Abstract

Previous functional integral methods for translationally invariant systems have been extended to the case of a confining trap potential. Essentially all finite-temperature properties of the repulsive Bose gas in a paraboloidal trap can be determined this way. New analytical results reported here are for the finite-temperature two-point correlation functions below the critical temperatures in d=3,2 and 1 dimensions. Only for d=3 are correlations both long range and coherent - at long range consistent with the existence of a coherent state of the condensate in the trap. The two-dimensional condensate is marginally stable in the sense that correlations decay by a power law.

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N. M. Bogoliubov, R. K. Bullough, V. S. Kapitonov, C. Malyshev, J. Timonen. 1999-10-27. Finite-temperature correlations in the trapped Bose gas. https://arxiv.org/abs/cond-mat/9910439

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