Vortex lattices in rotating Bose-Einstein condensates

The structure of the vortex lattice for a fast rotating condensate in a harmonic trap has been studied experimentally and numerically: it is an almost regular hexagonal lattice, with a distortion on the edges. In this paper, we provide rigorous proofs of results announced in [ A. Aftalion, X. Blanc, and J. Dalibard, Phys. Rev. A, 71 ( 2005), p. 023611]. We analyze the vortex pattern in the framework of the Gross - Pitaevskii energy using wave functions in the lowest Landau level. We compute the energy of a regular triangular lattice and of a class of distorted lattices and find the optimal distortion which provides a decay of the wave function similar to an inverted parabola.