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Quantum Arnol'd diffusion in a simple nonlinear system.
V Ya Demikhovskii1, F M Izrailev, A I Malyshev
1Nizhny Novgorod State University, Gagarin Avenue 23, Russia.
Summary
This study explores quantum Arnol'd diffusion in coupled nonlinear oscillators. Quantum diffusion is slower than classical, with dynamical localization observed, revealing new quantum dynamics in perturbed systems.
Area of Science:
- Quantum dynamics
- Nonlinear systems
- Chaos theory
Background:
- Arnol'd diffusion in classical systems arises from weak chaos near resonance separatrices.
- Understanding quantum analogues of classical chaotic phenomena is crucial for advancing quantum mechanics.
Purpose of the Study:
- Investigate the quantum fingerprint of Arnol'd diffusion in a two-coupled nonlinear oscillator system.
- Compare quantum diffusion characteristics with classical predictions.
- Identify novel quantum dynamical behaviors such as dynamical localization.
Main Methods:
- Analysis of a quantum system of two coupled nonlinear oscillators.
- Application of a two-frequency external force.
- Examination of the quantum diffusion coefficient and its dependence on model parameters.
Main Results:
- Quantum diffusion coefficient globally mimics classical data but is slower.
- Observed dynamical localization leading to diffusion saturation.
- Demonstrated that this localization shares nature with previously studied phenomena in global chaos.
Conclusions:
- Quantum Arnol'd diffusion is a distinct type of quantum dynamics.
- This phenomenon can be observed in systems like perturbed quantum billiards.
- The study provides insights into the quantum-classical correspondence in chaotic systems.