The standard approach to the calculation of the electronic structure in disordered solids is the mean-field, coherent-potential approximations. Although rather successful for electronic spectra, this approximation fails in the description of backscattering effects on transport properties. We applied an expansion beyond the mean-field approximation and evaluated the leading-order vertex corrections to the electrical conductivity for electrons scattered either on quenched random or thermally equilibrated impurities. We demonstrated that the sign of the vertex corrections to the Drude conductivity is in both cases negative. Quantum coherence due to elastic back-scatterings hence always leads to diminution of charge diffusion and localization effects.
