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Bosons à basse température: des intégrales de chemin aux gaz quasi-bidimensionnels

Abstract : This thesis deals with the Bose gas at low temperature. The first part presents the mathematical relationship between Bose-Einstein condensation and the group of permutations in the path-integral representation of the bosonic partition function. For an ideal Bose gas, Bose-Einstein condensation is found to be equivalent to a non-zero probability of finding infinite permutation cycles. The discussion is extended to the interacting Bose gas, and to the study of superfluidity. The second part concentrates on the quasi-two-dimensional ultra-cold atomic Bose gas which has been the object of recent experiments. Its description in terms of permutation cycles has allowed us to clarify the role of residual thermal excitations in the tightly confined perpendicular direction. A mean-field model which accounts for the occupation of the excited states in the third dimension agrees with the density profiles obtained experimentally and numerically, above the critical temperature. The deviations from mean-field theory are studied in the vicinity of the Kosterlitz-Thouless transition, where the gas enters a degenerate regime with strong pair-correlation effects.
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Contributor : Maguelonne Chevallier <>
Submitted on : Thursday, January 7, 2010 - 4:46:12 PM
Last modification on : Thursday, December 10, 2020 - 12:37:17 PM
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  • HAL Id : tel-00445117, version 1


Maguelonne Chevallier. Bosons à basse température: des intégrales de chemin aux gaz quasi-bidimensionnels. Matière Condensée [cond-mat]. Université Pierre et Marie Curie - Paris VI, 2009. Français. ⟨tel-00445117⟩



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