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Quantum-classical correspondence in localization of eigenstates for a system having mixed-type classical dynamics
1Department of Physics, Korea Advanced Institute of Science and Technology, Taejon 305-338, Korea.
Summary
We studied quantum eigenstates in systems with mixed classical dynamics. Strong localization relates to classical motion on Kolmogorov-Arnold-Moser tori, while weak localization arises from classical dynamics, not quantum effects.
Area of Science:
- Quantum mechanics
- Classical dynamics
- Statistical physics
Background:
- Understanding quantum localization is crucial for various physical systems.
- Mixed-type classical dynamics present unique challenges in quantum analysis.
- Kolmogorov-Arnold-Moser (KAM) tori are key structures in classical chaos theory.
Purpose of the Study:
- To investigate the localization properties of quantum eigenstates.
- To analyze the structure of eigenfunctions and spectral density of states.
- To differentiate between quantum and classical origins of localization phenomena.
Main Methods:
- Examination of quantum eigenstate localization.
- Analysis of eigenfunctions and local spectral density of states.
- Correlation with classical motion on Kolmogorov-Arnold-Moser tori.
Main Results:
- Strongly localized eigenstates are explained by classical motion on KAM tori.
- Weak localization of nearly delocalized eigenstates is a result of classical dynamics.
- Distinction between dynamical localization (quantum) and classical dynamics-induced localization.
Conclusions:
- Classical dynamics significantly influence quantum eigenstate localization.
- KAM tori provide a framework for understanding strong localization.
- Weak localization phenomena in these systems are primarily classical in origin.