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/ε^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 |log ε| \ll \Omega \ll 1/(ε^2|log ε|) with ε → 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.