The critical velocity for vortex existence in a two-dimensional rotating Bose–Einstein condensate

We investigate a model corresponding to the experiments for a two-dimensional rotating Bose–Einstein condensate. It consists in minimizing a Gross–Pitaevskii functional defined in R2 under the unit mass constraint. We estimate the critical rotational speed 1 for vortex existence in the bulk of the condensate and we give some fundamental energy estimates for velocities close to 1. © 2005 Elsevier Inc. All rights reserved.