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Issue ESAIM: Proc. Volume 27, 2009 CANUM 2008 Page(s) 1 - 14 DOI 10.1051/proc/2009017 Published online 25 June 2009

ESAIM: Proc., 2009, Vol. 27, pp. 1-14
DOI: 10.1051/proc/2009017

Anisotropy and vortices in Bose Einstein condensates

Amandine Aftalion

CNRS, Université Pierre et Marie Curie-Paris6, UMR 7598, Laboratoire Jacques-Louis Lions, 175 rue du Chevaleret, Paris F-75013 France

Published online: 25 June 2009

Abstract
The fast rotation of a Bose Einstein condensate in a harmonic trap leads to a hexagonal lattice of vortices, called the Abrikosov lattice. Vortices are described as the zeros of the condensate wave function, which is a solution to a nonlinear Schrödinger equation type. We study the solutions of this equation on a specific eigenspace of the limiting problem, the Lowest Landau Level. Upper and lower bounds for the energy allow to determine the presence of a vortex lattice or the lack of visible vortices, as a function of the anisotropy and the rotation. The study of the critical regime is open and would need some numerical simulations. This constitutes a project in collaboration with Xavier Blanc and Nicolas Lerner.

© EDP Sciences, ESAIM 2009

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