  Within a two-band tight binding model, we investigate the dynamics of
electrons with Markoffian dephasing under the influence of static electric
fields. With the help of both numerical and analytic calculations we find that
the dephasing ultimately takes electrons which are initially 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 intervention of dephasing. We also
obtain the effective decay time for the approach to equal band populations
under conditions of small interband communication and in the long-time limit,
through a perturbative calculation. The decay rate shows characteristic sharp
peaks at values of the parameters which give Zener resonances.
