Dipole oscillations in a Bose-Fermi mixture in the time-dependent approach

We study the dipole collective oscillations in a Bose-Fermi mixture, which are formulated with the time-dependent Gross-Pitaevskii equation and the Vlasov equation, using a dynamical time-dependent approach. We find a large difference in the behavior of fermion oscillations between the time-dependent approach and the usual approaches such as the random-phase approximation. The dipole oscillation of the Bose-Fermi mixture cannot be described with simple center-of-mass motions of the two gases.