Exact formulae for the electrical resistivity

Abstract

The theory of exact formulae for the electrical resistivity is reviewed. The derivation of an exact formula for the resistivity and the proof of the equivalence of this formula with the linear response formula for the electrical conductivity are presented. One form of the resistivity formula is evaluated in the limit of weak scattering. The model for this calculation is a system of non-interacting free electrons scattered by random fixed impurities. It is shown that the evidence which suggested that the resistivity formula is simpler to evaluate than the conductivity formula is misleading.