Semiclassical analysis of collective excitations in Bose-Einstein condensate

We investigate the low-lying excitations of Bose-Einstein condensate of confined alkali-metal atoms, with repulsive interaction. Vortex excitation energy of the condensate containing a large number of atoms is estimated semiclassically. We also investigate the asymptotic form of the low-energy quasiparticle excitation of the condensate in the presence of a vortex, in the large-N limit. The dispersion relation remains the same as that of a condensate without a vortex, except the z component of angular momentum of the modes is shifted by the angular momentum of the vortex. The first-order correction of the energy eigenvalues due to finite-size effects is calculated.