Comment on ``Fragmented Condensate Ground State of Trapped Weakly Interacting Bosons in Two Dimensions"

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Recently Liu et al. [PRL 87, 030404 (2001)] examined the lowest state of a weakly-interacting Bose-Einstein condensate. In addition to other interesting results, using the method of the pair correlation function, they questioned the validity of the mean-field picture of the formation of vortices and stated that the vortices are generated at the center of the cloud. This is in apparent contradiction to the Gross-Pitaevskii approach, which predicts that the vortices successively enter the cloud from its outer parts as L/N (where N is the number of atoms in the trap and hbar(L) is the angular momentum of the system) increases. We have managed to reproduce the results of Liu et al. however a more careful analysis presented below confirms the validity of the mean-field approach.