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American Institute of Mathematical Sciences (AIMS), Kinetic and Related Models, 3(10), p. 553-571, 2017

DOI: 10.3934/krm.2017022

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

Journal article published in 2015 by Loïc Le Treust, Weizhu Bao ORCID, Florian Méhats, Loïc Le Treust
This paper is made freely available by the publisher.
This paper is made freely available by the publisher.

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Abstract

We study dimension reduction for the three-dimensional Gross-Pitaevskii equation with a long-range and anisotropic dipole-dipole interaction modeling dipolar Bose-Einstein condensation in a strong interaction regime. The cases of disk shaped condensates (confinement from dimension three to dimension two) and cigar shaped condensates (confinement to dimension one) are analyzed. In both cases, the analysis combines averaging tools and semiclassical techniques. Asymptotic models are derived, with rates of convergence in terms of two small dimensionless parameters characterizing the strength of the confinement and the strength of the interaction between atoms.