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Quantum localization of chaotic eigenstates and the level spacing distribution
Benjamin Batistić1, Marko Robnik1
1CAMTP - Center for Applied Mathematics and Theoretical Physics, University of Maribor, Krekova 2, SI-2000 Maribor, Slovenia, European Union.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|December 17, 2013
Summary
We introduce new measures for quantum localization in chaotic systems. These measures correlate with spectral statistics, revealing a functional relationship in quantum chaos.
Area of Science:
- Quantum mechanics
- Quantum chaos
- Wave mechanics
Background:
- Quantum localization in classically chaotic eigenstates is a key problem in quantum chaos.
- Understanding this phenomenon is crucial for general quantum and wave mechanics.
- Spectral statistics are a fundamental aspect of quantum chaos.
Purpose of the Study:
- To propose and characterize two novel measures for quantum localization.
- To investigate the relationship between these localization measures and spectral statistics.
- To apply the developed approach to mixed-type billiard systems.
Main Methods:
- Development of two distinct localization measures: one based on information entropy, the other on Husimi function correlations.
- Analysis of the functional relationship between localization measures and spectral statistics exponent (β).
- Application to a mixed-type billiard system to differentiate regular and chaotic eigenstates.
Main Results:
- A clear functional relationship is established between the spectral statistics exponent (β) and the proposed localization measures.
- The two proposed localization measures are shown to be linearly equivalent.
- The study demonstrates how fractional power-law repulsion in energy levels is linked to quantum localization.
Conclusions:
- The proposed localization measures effectively quantify the degree of quantum localization in chaotic systems.
- The findings provide a deeper understanding of the interplay between localization and spectral statistics in quantum chaos.
- The developed methodology is general and applicable to various quantum chaotic systems, including mixed-type billiards.
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