Transport equation for weakly localized electrons

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Abstract
The weak-localization regime is usually cited as an example of the breakdown of the Boltzmann equation. Using the techniques of quantum transport theory, we generalize the Boltzmann equation to include the coherent backscattering associated with weak localization. The new transport equation includes, in addition to the usual impurity scattering, a backscattering which occurs on the time scale of the phase-coherence lifetime. All the standard weak-localization magnetoresistance results can be reproduced by properly modifying this term. One effect which is nonlinear in the electric field is also calculated.