Primary reference: http://www.tcm.phy.cam.ac.uk/~bds10/publications/lesh.ps.gz
Disorder is very important in the so-called mesoscopic regime, where the sample size is larger than the coherence length of electrons, and the coherence length is much larger than the Compton wavelength. Roughly speaking, due to the multiple scattering which occurs across the entire sample, transport is a diffusive process, but the scattering centres (i.e. impurities) are dilute and/or weak so that electrons propagate coherently between close ones.
One can imagine trying to compute the probability of transmission as the square of a propagator/two-point correlation function. Using field integral methods, one finds that the probability corresponds to a Feynmann diagram which contains a path going forwards then backwards. In particular, for the phases to not strongly cancel, the paths need to remain within a Compton wavelength of each other. The introduction of scattering centres gives rise to a quantum phenomenon where one can get a constructive interference by making a loop somewhere in the middle and making the forward and return paths go in the same direction instead.
The introduction of an intermediate length scale also introduces new effective modes, the most important of which are the diffuson (the classical diffusive mode) and the cooperon which is purely quantum mechanical (and corresponds roughly to the description above of forward and backward paths going in the same direction). The field theory then allow you to join these together arbitrarily and resumming the entire series then predicts various interesting phenomenon.
This post imported from StackExchange Physics at 2014-04-01 17:32 (UCT), posted by SE-user genneth