  Dynamic response of the F=2 spinor Bose-Einstein condensate (BEC) under the
influence of external magnetic fields is studied. A general formula is given
for the oscillation period to describe population transfer from the initial
polar state to other spin states. We show that when the frequency and the
reduced amplitude of the longitudinal magnetic field are related in a specific
manner, the population of the initial spin-0 state will be dynamically
localized during time evolution. The effects of external noise and nonlinear
spin exchange interaction on the dynamics of the spinor BEC are studied. We
show that while the external noise may eventually destroy the Rabi oscillations
and dynamic spin localization, these coherent phenomena are robust against the
nonlinear atomic interaction.
