Collective dynamics of vortices in trapped Bose-Einstein condensates

We have calculated collective-mode spectra for three-dimensional, rotating Bose-Einstein condensates in oblate harmonic traps using the microscopic Bogoliubov-de Gennes field theory. For condensates with Nv vortices, Nv Kelvin-Tkachenko-mode branches are obtained. The features of these modes are compared with those predicted by a classical point-vortex model. We have created movies to visualize the motion of the vortices corresponding to the Kelvin-Tkachenko waves.