Dynamic structure factor of a superfluid Fermi gas

We describe the excitation spectrum of a two-component neutral Fermi gas wi th attractive interactions in the superfluid phase at finite temperature by deriving a suitable Random-Phase approximation in the collisionless regime with the technique of functional derivatives. The obtained spectrum for th e homogeneous gas at small wavevectors contains the Bogoliubov-Anderson pho non and is essentially different from the spectrum predicted by the static Bogoliubov theory, which instead shows an unphysically large response. We a dapt the results for the homogeneous system to obtain the dynamic structure factor of a harmonically confined superfluid and we identify in the spectr um a unique feature of the superfluid phase.