Weakly interacting Bose-Einstein condensates under rotation: Mean-field versus exact solutions

We consider a weakly interacting, harmonically trapped Bose-Einstein conden sed gas under rotation and investigate the connection between the energies obtained from mean-field calculations and from exact diagonalizations in a subspace of degenerate states. From the latter we derive an approximation s cheme valid in the thermodynamic limit of many particles. Mean-field result s are shown to emerge as the correct leading-order approximation to exact c alculations in the same subspace.