Transport properties of 1D tight-binding disordered models: the Hamiltonian map approach

摘要

A Hamiltonian method is developed for the study of transport properties of one-dimensional (1D) tight-binding models with random potentials. It is based on an exact transformation of the discrete Schrodinger equation to a two-dimensional Hamiltonian map describing a classical linear oscillator under random parametric delta-kicks. We are interested in the statistical properties of the transmission coefficient T-L of a disordered sample of length L. In the ballistic regime we derive formulas for the mean value of the transmission coefficient T-L, its second moment and the variance, that are more accurate than the ones existing in the literature. In the localized regime we calculate statistical characteristics of In T-L, and demonstrate that its distribution function approaches the Gaussian form if L --> infinity. We demonstrate that single parameter scaling holds under certain conditions that follow from the analysis of the statistical properties of the classical trajectories. (C) 2004 Elsevier B.V. All rights reserved.