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Journal Articles Nonlinearity Year : 2015

Dimension reduction for anisotropic Bose-Einstein condensates in the strong interaction regime

Abstract

We study the problem of dimension reduction for the three dimensional Gross-Pitaevskii equation (GPE) describing a Bose-Einstein condensate confined in a strongly anisotropic harmonic trap. Since the gas is assumed to be in a strong interaction regime, we have to analyze two combined singular limits: a semi-classical limit in the transport direction and the strong partial confinement limit in the transversal direction. We prove that both limits commute together and we provide convergence rates. The by-products of this work are approximated models in reduced dimension for the GPE, with a priori estimates of the approximation errors.

Dates and versions

hal-00959084 , version 1 (13-03-2014)

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Weizhu Bao, Loïc Le Treust, Florian Méhats. Dimension reduction for anisotropic Bose-Einstein condensates in the strong interaction regime. Nonlinearity, 2015, 28 (3), pp.755-772. ⟨10.1088/0951-7715/28/3/755⟩. ⟨hal-00959084⟩
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