One-dimensional quantum models with correlated disorder versus classical oscillators with colored noise.
We perform an analytical study of the correspondence between a classical oscillator with frequency perturbed by a colored noise and the one-dimensional Anderson-type model with weak correlated diagonal disorder. It is rigorously shown that localization of electronic states in the quantum model corresponds to exponential divergence of nearby trajectories of the classical random oscillator. We discuss the relation between the localization length for the quantum model and the rate of energy growth for the stochastic oscillator. Finally, we examine the problem of electron transmission through a finite disordered lattice by considering the evolution of the classical oscillator.
Tessieri
L
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Department of Chemistry, Simon Fraser University, Burnaby, British Columbia, Canada V5A 1S6.
Izrailev
F M
FM