Volume 55, Number 6, September II 2001
|Page(s)||755 - 761|
|Published online||01 December 2003|
Finite-temperature correlations in the trapped Bose-Einstein gas
Steklov Institute of Mathematics at St. Petersburg Fontanka 27,
191011 St. Petersburg, Russia
2 Department of Mathematics, The University of Manchester Institute of Science and Technology - P.O. Box 88, Manchester M60 1QD, UK
3 St. Petersburg Technological Institute Moskovsky 26, 196013 St. Petersburg, Russia
4 Department of Physics, University of Jyväskylä P.O. Box 35, FIN-40351 Jyväskylä, Finland
Accepted: 27 June 2001
New analytical results are reported for the two-point correlation function at nonzero temperatures in d=3,2 and 1 dimensions. Only for d=3 are correlations below Tc both long range and coherent —at long range consistent with the existence of a coherent state of the condensate in the trap. Asymptotically these correlations are found to decay as towards a nonzero value. The condensate density , with , is a slowly varying function and introduces a small amplitude variation in the decay of correlations when considered as a function of . The prediction of a -dependence at least has very recently been confirmed in a beautiful experiment (Bloch I., Hänsch T. W. and Esslinger T. REVIEWNature4032000166). The two-dimensional condensate is marginally stable in the sense that for correlations decay by a power law.
PACS: 03.75.Fi – Phase coherent atomic ensembles; quantum condensation phenomena / 05.30.Jp – Boson systems
© EDP Sciences, 2001
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