  We numerically study the parametric pumped current when magnetic field is
applied both in the adiabatic and non-adiabatic regimes. In particular, we
investigate the nature of pumped current for systems with resonance as well as
anti-resonance. It is found that in the adiabatic regime, the pumped current
changes sign across the sharp resonance with long lifetime while the
non-adiabatic pumped current at finite frequency does not. When the lifetime of
resonant level is short, the behaviors of adiabatic and non-adiabatic pumped
current are similar with sign changes. Our results show that at the energy
where complete transmission occurs the adiabatic pumped current is zero while
non-adiabatic pumped current is non-zero. Different from the resonant case,
both adiabatic and non-adiabatic pumped current are zero at anti-resonance with
complete reflection. We also investigate the pumped current when the other
system parameters such as magnetic field, pumped frequency, and pumping
potentials. Interesting behaviors are revealed. Finally, we study the symmetry
relation of pumped current for several systems with different spatial symmetry
upon reversal of magnetic field. Different from the previous theoretical
prediction, we find that a system with general inversion symmetry can pump out
a finite current in the adiabatic regime. At small magnetic field, the pumped
current has an approximate relation I(B) \approx I(-B) both in adiabatic and
non-adiabatic regimes.
