Volume 27, 2009CANUM 2008
|Page(s)||1 - 14|
|Published online||25 June 2009|
Anisotropy and vortices in Bose Einstein condensates
CNRS, Université Pierre et Marie Curie-Paris6, UMR 7598, Laboratoire Jacques-Louis Lions, 175 rue du Chevaleret, Paris F-75013 France
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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