Dissipative Transitions between Bloch Bands

We study the effect of dissipative transport of two-band systems in a static electric field. With the help of numerical solutions of a stochastic Liouville equation for the density matrix, we find that the Markoffian dephasing will take electrons, which are initially located in one band to equal population of the two bands, instead of undergoing Zener resonance, as they do in the absence of scattering.