  The spin mixing dynamics of spin-1 Bose-Einstein condensates with zero
magnetization and under an external magnetic field is investigated. The
time-dependent solutions are obtained via a diagonalization of the Hamiltonian,
which has a simple form under the single mode approximation. The features of
evolution are compared in detail with those with the field removed so as to
emphasize the effect of the field, which can induce strong oscillation in
population of atoms in spin component 0 . A new mode of oscillation
characterized by a high frequency and a low frequency, is found when the field
is sufficiently strong.
