  Time-dependent density-functional theory (TDDFT) is a powerful tool to study
the non-equilibrium dynamics of inhomogeneous interacting many-body systems.
Here we show that the simple adiabatic local-spin-density approximation for the
time-dependent exchange-correlation potential is surprisingly accurate in
describing collective density and spin dynamics in strongly correlated
one-dimensional ultracold Fermi gases. Our conclusions are based on extensive
comparisons between our TDDFT results and accurate results based on the
adaptive time-dependent density-matrix renormalization-group method.
