Dimension reduction for rotating Bose-Einstein condensates with anisotropic confinement

Florian Méhats; Christof Sparber

doi:10.3934/dcds.2016021

Article Contents

2016, Volume 36, Issue 9: 5097-5118. Doi: 10.3934/dcds.2016021

This issue Previous Article Correlation integral and determinism for a family of $2^\infty$ maps Next Article A new class of 3-dimensional piecewise affine systems with homoclinic orbits

Dimension reduction for rotating Bose-Einstein condensates with anisotropic confinement

Florian Méhats^1, and
Christof Sparber^2,

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: June 30, 2015

Revised: January 31, 2016

Published: May 2017

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Abstract

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.

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Mathematics Subject Classification: Primary: 35Q55; Secondary: 35B25.

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