Low-lying excitations of a trapped rotating Bose-Einstein condensate

We investigate the low-lying excitations of a weakly interacting, harmonically trapped Bose-Einstein condensed gas under rotation, in the limit where the angular mometum L of the system is much less than the number of the atoms N in the trap. We show that in the asymptotic limit $\overrightarrow{N}\infty$ the excitation energy, measured from the energy of the lowest state, is given by ${27N}_3{(N}_3-{1)v}_0/68,$ where $N_3$ is the number of octupole excitations, and $v_0$ is the unit of the interaction energy.