Algebraic technique for the transport and optical properties of electrons in a random array of strong scattering centers

Abstract

We develop an algebraic technique for the evaluation of the coefficients of a general transport equation for dynamically independent electrons in the presence of random impurities. This method readily yields, for arbitrarily strong single center potentials, these coefficients in powers of the density of the impurities. There is no restriction, in these calculations, on the wave vector or frequency of the external electric field. We explicitly give the coefficients of the transport equation up to first order in the impurity density and study in detail the case of free electrons. For short-range scatterers we obtain, in this case, a closed expression for the transverse conductivity.