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La transition de Bose-Einstein dans un gaz dilué

Abstract : In this thesis I study the influence of the inter-particle interactions on the Bose-Einstein phase transition of a dilute gas, where the collisional properties are characterized by the scattering length a. One part of my work concerns the calculation of the critical temperature in an homogeneous system. Within various --analytical and numerical-- approaches I show that the interactions give rise to a shift of the critical temperature linear in a. Combining perturbation theory with a quantum Monte-Carlo calculation, the value of the critical temperature is determined in the very dilute limit. In a second part I present the results of my quantum Monte Carlo calculations corresponding to current experiments for N = 10 000 bosons trapped in a harmonic potential. The concept of non-diagonal long-range order of the condensate allows to determine the condensate fraction and the condensate wave function in this inhomogeneous, interacting system. Quantitative comparisons of the Monte Carlo calculation with simple approximations show the limits of mean field approximations and allow to estimate the effects of correlations for trapped gases.
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Submitted on : Tuesday, March 7, 2006 - 11:27:58 AM
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  • HAL Id : tel-00011774, version 1


Markus Holzmann. La transition de Bose-Einstein dans un gaz dilué. Physique Atomique [physics.atom-ph]. Université Pierre et Marie Curie - Paris VI, 2000. Français. ⟨tel-00011774⟩



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