Macroscopic dynamics of a Bose-Einstein condensate containing a vortex lattice

Starting from the equations of rotational hydrodynamics we study the macroscopic behavior of a trapped Bose-Einstein condensate containing a large number of vortices. The stationary configurations of the system, the frequencies of the collective excitations, and the expansion of the condensate are investigated as a function of the angular velocity of the vortex lattice. The time evolution of the condensate and of the lattice geometry induced by a sudden deformation of the trap is also discussed and compared with the recent experimental results of P. Engels et al. [Phys. Rev. Lett. 89, 100403 (2002)].