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

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 Schrödinger 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 TLTL of a disordered sample of length LL. In the ballistic regime we derive formulas for the mean value of the transmission coefficient TLTL, 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 View the MathML sourcelnTL, and demonstrate that its distribution function approaches the Gaussian form if L→∞L→∞. We demonstrate that single parameter scaling holds under certain conditions that follow from the analysis of the statistical properties of the classical trajectories.