Resistance of a one-dimensional finite chain of periodically arranged random scatterers

Abstract

The electron resistance of a one-dimensional chain of random scatterers located at the same distance to each other is considered. The localization length for uniformly distributed amplitudes of the delta-function was analytically calculated without the assumption of weak scattering. It is shown that Landauer's resistance of chain increases not exponentially but, generally speaking, by a “power” law with increasing chain length for an electron energy corresponding to the center of the zone. In the weak disordered limit the well-known relation ln 〈〉 = 2〈ln〉 takes place. In the other limiting case of strong scattering this relation does not take place.