  We study quadrupole collective oscillations in the bose-fermi mixtures of
ultracold atomic gases of Yb isotopes, which are realized by Kyoto group. Three
kinds of combinations are chosen, Yb170-Yb171, Yb170-Yb173 and Yb174-Yb173,
where boson-fermion interactions are weakly repulsive, strongly attractive and
strongly repulsive respectively. Collective oscillations in these mixtures are
calculated in a dynamical time-evolution approach formulated with the
time-dependent Gross-Pitaevskii and the Vlasov equations. The boson
oscillations are shown to have one collective mode, and the fermions are shown
to have the boson-forced and two intrinsic modes, which correspond to the
inside- and outside-fermion oscillations for the boson-distributed regions. In
the case of the weak boson-fermion interactions, the dynamical calculations are
shown to be consistent with the results obtained in the small amplitude
approximations as the random phase approximation in early stage of oscillation,
but, in later stage, these two approaches are shown to give the different
results. Also, in the case of the strong boson-fermion interactions,
discrepancies appear in early stage of oscillation. We also analyze these
differences in two approaches, and show that they originated in the change of
the fermion distributions through oscillation.
