SCATTERING-THEORY, TRANSFER-MATRICES, AND ANDERSON LOCALIZATION

We discuss the scattering theory of quantum transport, in which properties of a disordered sample connected to ideal, multichannel leads are expressed in terms of its transfer matrix, T. Taking a continuum limit in which the sample is divided into many thin slices, the Lyapunov exponents, characterizing the dependence of T on sample length, are calculated in terms of the probability distribution of the eigenvectors of TT(dagger). It is shown that localization of these eigenvectors accompanies the disorder-induced metal-insulator transition, and an approximation scheme is developed to study the transition.