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Quantum manifestations of classical nonlinear resonances
Diego A Wisniacki1, Peter Schlagheck2
1Departamento de Física and IFIBA, FCEyN, UBA Ciudad Universitaria, Pabellón 1, Ciudad Universitaria, 1428 Buenos Aires, Argentina.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|January 15, 2016
Summary
Quantum mechanics reveals how nonlinear resonances disrupt energy levels in the standard map, leading to chaos. These resonances systematically influence quantum state localization, offering insights into quantum chaos.
Area of Science:
- Quantum chaos
- Statistical mechanics
- Nonlinear dynamics
Background:
- Integrable classical systems, when perturbed, exhibit nonlinear resonances that evolve and disappear due to chaos.
- Understanding the quantum manifestations of these classical phenomena is crucial for a complete picture of chaotic dynamics.
Purpose of the Study:
- To investigate the quantum effects of nonlinear resonances in the standard map.
- To analyze how these resonances perturb quantum states and influence their properties.
Main Methods:
- Studying the standard map as a model system.
- Analyzing the breaking of eigenphase degeneracies in quantum states.
- Employing semiclassical expressions derived from integrable approximations of the Hamiltonian.
- Investigating the phase space morphology and localization properties of quantum states.
Main Results:
- Nonlinear resonances break eigenphase degeneracies for specific quantum states.
- Eigenphase splittings are accurately described by semiclassical expressions.
- Nonlinear resonances systematically influence the localization properties of quantum states in phase space.
Conclusions:
- Nonlinear resonances play a significant role in the quantum dynamics of the standard map.
- The study provides a framework for understanding quantum manifestations of classical chaos.
- Semiclassical methods are effective in describing resonance phenomena in quantum systems.
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