Oscillations of a bose-einstein condensate rotating in a harmonic plus quartic trap

We study the normal modes of a two-dimensional rotating Bose-Einstein condensate confined in a quadratic plus quartic trap. Hydrodynamic theory and sum rules are used to derive analytical predictions for the collective frequencies in the limit of high angular velocities Omega where the vortex lattice produced by the rotation exhibits an annular structure. We predict a class of excitations with frequency sqrt[6]Omega in the rotating frame, irrespective of the mode multipolarity m, as well as a class of low energy modes with frequency proportional to |m|/Omega. The predictions are in good agreement with results of numerical simulations based on the 2D Gross-Pitaevskii equation. The same analysis is also carried out at even higher angular velocities, where the system enters the giant vortex regime.