Energy and vorticity in fast rotating Bose-Einstein condensates

We study a rapidly rotating Bose-Einstein condensate confined to a finite trap in the framework of two-dimensional Gross-Pitaevskii theory in the strong coupling (Thomas-Fermi) limit. Denoting the coupling parameter by 1/epsilon(2) and the rotational velocity by Omega, we evaluate exactly the next to the leading-order contribution to the ground-state energy in the parameter regime vertical bar log epsilon vertical bar << Omega << 1/(epsilon(2)vertical bar log epsilon vertical bar) with epsilon -> 0. While the TF energy includes only the contribution of the centrifugal forces the next order corresponds to a lattice of vortices whose density is proportional to the rotational velocity.