# American Institute of Mathematical Sciences

September  2016, 36(9): 5097-5118. doi: 10.3934/dcds.2016021

## Dimension reduction for rotating Bose-Einstein condensates with anisotropic confinement

 1 IRMAR, Université de Rennes 1 and IPSO, INRIA Rennes, 35042 Rennes Cedex 2 Department of Mathematics, Statistics, and Computer Science, University of Illinois, Chicago, 851 South Morgan Street, Chicago, Illinois 60607

Received  July 2015 Revised  February 2016 Published  May 2016

We consider the three-dimensional time-dependent Gross-Pitaevskii equation arising in the description of rotating Bose-Einstein condensates and study the corresponding scaling limit of strongly anisotropic confinement potentials. The resulting effective equations in one or two spatial dimensions, respectively, are rigorously obtained as special cases of an averaged three dimensional limit model. In the particular case where the rotation axis is not parallel to the strongly confining direction the resulting limiting model(s) include a negative, and thus, purely repulsive quadratic potential, which is not present in the original equation and which can be seen as an effective centrifugal force counteracting the confinement.
Citation: Florian Méhats, Christof Sparber. Dimension reduction for rotating Bose-Einstein condensates with anisotropic confinement. Discrete & Continuous Dynamical Systems - A, 2016, 36 (9) : 5097-5118. doi: 10.3934/dcds.2016021
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