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Transport dans les condensats de Bose-Einstein uni-dimensionnels desordonnes

Abstract : This thesis presents a theoretical study of coherent transport phenomena in unidimensional Bose-Einstein condensates in presence of disorder. We devoted a particular attention to the nonlinear effects caused by the interactions between the atoms. In a first stage, we have studied the scattering of a dark soliton by a finite-size obstacle. We have developed a perturbative method which has enabled us to study the dynamics of the soliton and to determine the quantity of radiated energy during the scattering. We have then applied this approach to the study of the propagation of a soliton in presence of a random succession of point-like obstacles. We have shown that the soliton is accelerated until until it reaches the speed of sound and then disappears. Its decay is not exponential but algebraic and the distance covered by the soliton in the disordered region before decaying is independant of its initial speed. Finally, we have studied the "fate" of the radiations emitted during the scattering of the soliton.This has led us to study the localization's properties of elementary excitations in a disordered condensate. We have used two methods (one based on the phase formalism and the other on the transfer matrix approach ) which allowed us to determine the localization length at low energy in the first case and for all the range of energy in the second. We obtained, at low and high energy, a behavior similar to that of phonons and without interaction particles respectively.
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https://tel.archives-ouvertes.fr/tel-00083364
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Submitted on : Friday, June 30, 2006 - 1:52:35 PM
Last modification on : Wednesday, September 16, 2020 - 4:05:05 PM
Long-term archiving on: : Tuesday, September 18, 2012 - 3:26:01 PM

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Nicolas Bilas. Transport dans les condensats de Bose-Einstein uni-dimensionnels desordonnes. Physique mathématique [math-ph]. Université Paris Sud - Paris XI, 2006. Français. ⟨tel-00083364⟩

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