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.
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