Monopole oscillations and dampings in a boson and fermion mixture in the time-dependent Gross-Pitaevskii and Vlasov equations

We construct a dynamical model for the time evolution of the boson-fermion coexistence system. The dynamics of bosons and fermions are formulated with the time-dependent Gross-Pitaevsky equation and the Vlasov equation. We thus study the monopole oscillation in the boson-fermion mixture. We find that large damping exists for fermion oscillations in the mixed system even at zero temperature.