Vertex corrections to the electrical conductivity in models with elastically scattered electrons

We study quantum coherence of elastically scattered lattice fermions. We calculate vertex corrections to the electrical conductivity of electrons scattered either on thermally equilibrated or statically distributed random impurities. We demonstrate that the sign of the vertex corrections to the Drude conductivity is in both cases negative. Quantum coherence due to elastic back scatterings always leads to diminution of diffusion.