Dipole Oscillations in Bose - Fermi Mixture in the Time-Dependent Grosspitaevskii and Vlasov equations

We study the dipole collective oscillations in the bose-fermi mixture using a dynamical time-dependent approach, which are formulated with the time-dependent Gross-Pitaevskii equation and the Vlasov equation. We find big difference in behaviors of fermion oscillation between the time-dependent approach and usual approaches such as the random-phase approximation and the sum-rule approach. While the bose gas oscillates monotonously, the fermion oscillation shows a beat and a damping. When the amplitude is not minimal, the dipole oscillation of the fermi gas cannot be described with a simple center-of-mass motion.