Resistance of a 1D random chain: Hamiltonian version of the transfer matrix approach

TL;DR

This paper introduces a novel Hamiltonian-based transfer matrix method to analyze electron transport resistance in disordered 1D chains, providing analytical insights into ballistic and localized regimes.

Contribution

It develops a new Hamiltonian map approach for the transfer matrix method, linking quantum electron transport to classical Hamiltonian dynamics.

Findings

Analytical expressions for mean resistance and its second moment in different regimes.

Demonstration of the Hamiltonian map approach in deriving transport properties.

Discussion of single-parameter scaling implications for resistance.

Abstract

We study some mesoscopic properties of electron transport by employing one-dimensional chains and Anderson tight-binding model. Principal attention is paid to the resistance of finite-length chains with disordered white-noise potential. We develop a new version of the transfer matrix approach based on the equivalency of a discrete Schroedinger equation and a two-dimensional Hamiltonian map describing a parametric kicked oscillator. In the two limiting cases of ballistic and localized regime we demonstrate how analytical results for the mean resistance and its second moment can be derived directly from the averaging over classical trajectories of the Hamiltonian map. We also discuss the implication of the single-parameter scaling hypothesis to the resistance.