Hydrodynamic excitations of trapped Fermi gases

We discuss collective excitations of a trapped dilute. Fermi gas within a h ydrodynamic approximation. Analytical results an derived for both high- and low-temperature limits and are applied to K-40 and Li-6 systems of current experimental interest. We identify,spectral :signatures which can be used to detect the onset of Fermi degeneracy. Also, we find an interesting::clas s of internal excitations with an unusual spectrum. Some of our results are relevant to the case of:;trapped bosons as well. Our analysis suggests sev eral experiments which address fundamental problems of,collective motion in quantum fluids.