Dynamic structure factor of a superfluid Fermi gas

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