%0 Journal Article
%T Dimension reduction for dipolar Bose-Einstein condensates in the strong interaction regime
%+ National University of Singapore (NUS)
%+ Invariant Preserving SOlvers (IPSO)
%A Bao, Weizhu
%A Le Treust, Loïc
%A Méhats, Florian
%Z This work was supported by the Ministry of Education of Singaporegrant R-146-000-196-112 (W.B.), by the ANR-FWF Project Lodiquas ANR-11-IS01-0003 (L.L.T. and F.M.), by the ANR-10-BLAN-0101 Grant (L.L.T.) andby the ANR project Moonrise ANR-14-CE23-0007-01 (F.M.).
%< avec comité de lecture
%@ 1937-5093
%J Kinetic and Related Models
%I AIMS
%V 10
%N 3
%P 553-571
%8 2017-09
%D 2017
%Z 1501.02177
%R 10.3934/krm.2017022
%K Partial Differential Equations
%K Dipolar Bose-Einstein Condensates
%K Semiclassical analysis
%K Averaging techniques
%Z 35Q55, 35Q40
%Z Mathematics [math]/Analysis of PDEs [math.AP]Journal articles
%X 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.
%G English
%2 https://hal.science/hal-01101793/document
%2 https://hal.science/hal-01101793/file/DBEC-Conf.pdf
%L hal-01101793
%U https://hal.science/hal-01101793
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