Monopole Oscillations and Dampings in 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 bose-fermi mixture. We find that large damping exists for fermion oscillations in the mixed system even at zero temperature.Comment: 16 pages text and 12 figure