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One-dimensional quantum models with correlated disorder versus classical oscillators with colored noise
1Department of Chemistry, Simon Fraser University, Burnaby, British Columbia, Canada V5A 1S6.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|December 12, 2001
Summary
We rigorously show that quantum electronic state localization in disordered systems corresponds to classical oscillator trajectory divergence. This study links quantum localization length to classical energy growth rates for disordered systems.
Area of Science:
- Quantum mechanics
- Statistical physics
- Condensed matter physics
Background:
- The Anderson model describes electronic localization in disordered systems.
- Classical oscillators perturbed by noise exhibit complex dynamics.
Purpose of the Study:
- To establish a rigorous analytical correspondence between quantum Anderson localization and classical stochastic oscillator behavior.
- To investigate the relationship between quantum localization length and classical energy growth.
Main Methods:
- Analytical study of a classical oscillator with colored noise.
- Comparison with the one-dimensional Anderson model with weak correlated diagonal disorder.
- Examination of electron transmission through a finite disordered lattice.
Main Results:
- Rigorous proof that quantum electronic state localization is equivalent to exponential divergence of classical random oscillator trajectories.
- Established a relationship between the localization length in the quantum model and the energy growth rate of the classical oscillator.
- Analyzed electron transmission by modeling classical oscillator evolution.
Conclusions:
- The study provides a novel analytical link between quantum localization phenomena and classical stochastic dynamics.
- Findings offer insights into electron transport in disordered materials by leveraging classical analogies.
- The classical oscillator model serves as a valuable tool for understanding quantum localization effects.