Transport properties of 1D disordered models: a novel approach

Abstract

A new method is developed for the study of transport properties of 1D models with random potentials. It is based on an exact transformation that reduces discrete Schrödinger equation in the tight-binding model to a two-dimensional Hamiltonian map. This map describes the behavior of 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 expressions for the mean value of the transmission coefficient $T_L$, its second moment and variance, that are more accurate than the existing ones. In the localized regime we analyze the global characteristics of $\ln T_L$, and demonstrate that its distribution function approaches the Gaussian form if $L\to \infty$. For any finite $L$ there are deviations from the Gaussian law that originate from the subtle correlation effects between different trajectories of the Hamiltonian map.

RevTex, 8 pages, 4 EPS-figures, corrected format

References in corpus (4)

• Band-center anomaly of the conductance distribution in one-dimensional Anderson localization
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• Onset of Delocalization in Quasi-1D Waveguides with Correlated Surface Disorder
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Cited by in corpus (5)

• Anomalous Localization in Low-Dimensional Systems with Correlated Disorder
• Anomalous transport in low-dimensional systems with correlated disorder
• Localization of weakly interacting Bose gas in quasiperiodic potential
• Resonant enhancement of Anderson localization: Analytical approach
• Universal Scaling of Electron Transmission for Nearly Ballistic and Quantum Dragon Nanodevices