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

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