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 corre...
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| Published in | Physical review. E, Statistical, nonlinear, and soft matter physics Vol. 64; no. 6 Pt 2; p. 066120 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
United States
01.12.2001
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| Online Access | Get more information |
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| Summary: | 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. |
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| ISSN: | 1539-3755 |
| DOI: | 10.1103/PhysRevE.64.066120 |