The anomalous resistivity increase

The anomalous resistivity increase is due to long-rangecorrelations in the diffusive motion of an electron that arepurely quantum mechanical. In the semiclassical theoryit is assumed that a few scattering events randomize theelectron velocity, so the velocity correlation function decaysexponentially in time with decay time τ [see Eq.(1.20)]. As discussed in Section I.D.3, this assumptionleads to the Drude formula for the resistivity. It is only inrecent years that one has come to appreciate that purelyelastic scattering is not effective in destroying correlationsin the phase of the electron wave function. Suchcorrelations lead to quantum interference corrections tothe Drude result, which can explain the anomalous increasein the resistivity at low temperatures.