Low-lying twisting and acoustic modes of a rotating Bose-Einstein condensate

We present a calculation of the low lying spectrum of a rotating Bose-Einstein condensate. We show that in a cylindrical geometry, there exist two linear branches, one associated with usual acoustic excitations, the other corresponding to a twisting mode of the vortex lattice. Using a hydrodynamical approach, we derive the elasticity coefficient of the vortex lattice and calculate the spectrum of condensate in a three-dimensional harmonic trap with cylindrical symmetry.