Condensation of interacting bosons in a random potential |
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Authors: | Robert Seiringer Jakob Yngvason Valentin A. Zagrebnov |
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Affiliation: | 11828. Department of Mathematics and Statistics, McGill University, 805 Sherbrooke Street West, Montreal, QC, H3A 2K6, Canada 21828. Fakult?t für Physik, Universit?t Wien, Boltzmanngasse 5, 1090, Vienna, Austria 31828. Département de Mathématiques, Université d’Aix-Marseille (AMU) and Centre de Physique Théorique – UMR 7332, Luminy Case 907, 13288, Marseille Cedex 09, France
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Abstract: | We study the effects of random scatterers on the ground state of the one-dimensional Lieb-Liniger model of interacting bosons on the unit interval. We prove that, in the Gross-Pitaevskii limit, Bose Einstein condensation takes place in the whole parameter range considered. The character of the wave function of the condensate, however, depends in an essential way on the interplay between randomness and the strength of the two-body interaction. For low density of scatterers or strong interactions the wave function extends over the whole interval. High density of scatterers and weak interaction, on the other hand, leads to localization of the wave function in a fragmented subset of the unit interval. |
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