Time-dependent density-functional theory for trapped strongly interacting fermionic atoms

The dynamics of strongly interacting trapped dilute two-component Fermi gases (dilute in the sense that the range of interatomic potential is small compared with interparticle spacing) is investigated in a single-equation approach to the time-dependent density-functional theory. For the ground-state energy per particle of the system in the homogeneous phase, we have constructed an Pade parametrization based on Monte Carlo data and asymptotic behavior. Our numerical results for collective frequencies in the BCS-BEC crossover regime are in good agreement with recent experimental data obtained by the Duke University group. In addition, we show that the calculated corrections to the hydrodynamic approximation may be important, even for systems with a rather large number of atoms.