The giant vortex state for a Bose-Einstein condensate in a rotating anharmonic trap : extreme rotation regimes.


Le document est une prépublication

Code(s) de Classification MSC:

Code(s) de Classification CR:


Abstract :We study the fast rotation limit for a Bose-Einstein condensate in a quadratic plus quartic confining potential within the framework of the two dimensional Gross-Pitaevskii energy functional. As the rotation speed tends to infinity with a proper scaling of the other parameters in the model, a linear limit problem appears for which we are able to derive precise energy estimates. We prove that the energy and density asymptotics of the problem can be obtained by minimizing a simplified one dimensional energy functional. In the case of a fixed coupling constant we also prove that a giant vortex state appears. It is an annulus with pure irrotational fl ow encircling a central low-density hole around which there is a macroscopic phase circulation.

Mots Clés: ;

Date: 2008-09-11