Within a two-band tight-binding model, we investigate the dynamics of
electrons with Markoffian dephasing under the influence of static elec
tric fields. With the help of both numerical and analytic calculations
we find that the dephasing ultimately takes electrons that are initia
lly located in one miniband to equal population of the two minibands,
instead of undergoing persistent Rabi flop, as they do in the absence
of scattering. Miniband localization is wholly destroyed by the interv
ention of dephasing. We also obtain the effective decay time for the a
pproach to equal band populations under conditions of small interband
communication and in the long-time limit, through a perturbative calcu
lation. The decay rate shows characteristic sharp peaks at values of t
he parameters that give Zener resonances. [S0163-1829(98)06116-5].