Stability of giant vortices in quantum liquids

We show how giant vortices can be stabilized in strong external potential Bose-Einstein condensates. We illustrate the formation of these vortices thanks to the relaxation Ginzburg-Landau dynamics for two typical potentials in two spatial dimensions. The giant vortex stability is studied for the particular case of the rotating cylindrical hard wall. The minimization of the perturbed energy is simplified into a one dimensional relaxation dynamics. The giant vortices can be stabilized only in a finite frequency range. Finally we obtain a curve for the minimum frequency needed to observe a giant vortex for a given nonlinearity.