Mode Coupling Theory for Impurity Conduction

Abstract

Equation (43.5) can be used as a starting point for the discussion of the localization of electrons by (arbitrary) random potentials in one and two dimensions and by sufficiently strong random potentials in three dimensions. An important point in this discussion is a “self-consistent feedback” contained in (43.5): the random potential modifies the density “propagator” Φ occurring in (43.5) from free-particle propagation Φ ₀ to diffusive-type propagation. This slowing down of the particle propagation leads to a slowing down of the random force fluctuations via (43.5) manifesting itself as a low-frequency increase of N(z), and a corresponding low-frequency decrease of σ(z) via (42.23) and (12.1) (see the first equation of the previous chapter).