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 flow encircling a central low-density hole around which there is a macroscopic phase circulation. © 2010 Elsevier Masson SAS.
Rougerie, N. (2011). The giant vortex state for a Bose-Einstein condensate in a rotating anharmonic trap: Extreme rotation regimes. Journal Des Mathematiques Pures et Appliquees, 95(3), 296–347. https://doi.org/10.1016/j.matpur.2010.11.004