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Delocalization and quantum chaos in atom-field systems.
M A Bastarrachea-Magnani1, B López-del-Carpio2, J Chávez-Carlos1
1Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, Apdo. Postal 70-543, México D. F., C.P. 04510, México.
Physical Review. E
|March 18, 2016
Summary
This study quantifies regular and chaotic behavior in the Dicke model, finding a strong link between classical Lyapunov exponents and quantum Participation Ratio. The ratio
Area of Science:
- Quantum optics
- Atomic physics
- Chaos theory
Background:
- The Dicke model is a fundamental system for studying atom-field interactions.
- Understanding the transition between regular and chaotic dynamics is crucial in quantum systems.
Purpose of the Study:
- To quantitatively investigate the regular and chaotic regions in the phase space of the Dicke model.
- To explore the correlation between classical and quantum measures of chaos.
Main Methods:
- Utilizing efficient diagonalization techniques for a detailed quantitative study.
- Analyzing phase space regions within the simplest nonintegrable atom-field system.
Main Results:
- A close correlation was found between classical Lyapunov exponents and the quantum Participation Ratio of coherent states.
- The Participation Ratio exhibits distinct scaling behaviors in regular and chaotic regimes.
Conclusions:
- The study establishes a quantitative link between classical and quantum chaos indicators in the Dicke model.
- The scaling properties of the Participation Ratio provide insights into the nature of regularity and chaos.
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