Localization in a Random System of <i>N</i> Coupled Chains I. Microscopic Model, General Scheme

Abstract

Abstract On the basis of a microscopic model describing the motion of an electron under the influence of a weak random potential in a system of N weakly coupled chains localization of all eigenstates for finite N is proved. Using Berezinskii's idea of ordering the diagrams along the chain the diagram analysis for this system with N states in each cross section and an effective method for treating this N 2 ‐variable problem are developed. The localization length is shown to be equal to Nl 2 ( l 2 mean free path for backward scattering at one chain). In the limit N → ∞ diffusion is obtained for d = 3.