1D quantum models with correlated disorder vs. classical oscillators with coloured noise

Details 1D quantum models with correlated disorder vs. classical oscillators with coloured noise 1D quantum models with correlated disorder vs. classical oscillators with coloured noise

2001-06-04

arxiv.org/abs/cond-mat/0106053v1

Physics

Condensed Matter

Disordered Systems and Neural Networks

23 pages, LaTeX file

Scientific paper

10.1103/PhysRevE.64.066120

We perform an analytical study of the correspondence between a classical oscillator with frequency perturbed by a coloured noise and the one-dimensional Anderson-type model with correlated diagonal disorder. It is rigorously shown that localisation 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 localisation 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 barrier by considering the evolution of the classical oscillator.

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