Elementary Excitations in Trapped Bose-Einstein Condensed Gases Beyond the Mean-Field Approximation

Using the hydrodynamic theory of superfluids and the Lee-Huang-Yang equation of state for interacting Bose gases, we derive the first correction to the collective frequencies of a trapped gas, due to effects beyond the mean field approximation. The corresponding frequency shift, which is calculated at zero temperature and for large $N$, is compared with other corrections due to finite size, nonlinearity, and temperature. We show that for reasonable choices of the relevant parameters of the system, the non-mean-field correction is the leading contribution and amounts to about $1\%$. The role of the deformation of the trap is also discussed.