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Using hydrodynamic theory of superfluids and the Lee-Huang-Yang equation ofstate for interacting Bose gases we derive the first correction to thecollective frequencies of a trapped gas, due to effects beyond mean fieldapproximation. The corresponding frequency shift, which is calculated at zerotemperature and for large N, is compared with other corrections due to finitesize, non-linearity and finite temperature. We show that for reasonable choicesof the relevant parameters of the system, the non-mean field correction is theleading contribution and amounts to about 1%. The role of the deformation ofthe trap is also discussed.Comment: 4 pages, 1 Postscript figur

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