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 $N\to \mathrm{\infty }$ the excitation energy, measured from the energy of the lowest state, is given by $27N_3(N_3-1)v_0\mathrm{/}68$, where $N_3$ is the number of octupole excitations and $v_0$ is the unit of the interaction energy.