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Quantum coherence, evolution of the Wigner function, and transition from quantum to classical dynamics for a chaotic
1L. V. Kirensky Institute of Physics, 660036 Krasnoyarsk, Russia.
Chaos (Woodbury, N.Y.)
|December 1, 1996
Summary
Quantum systems lose coherence due to environmental influence, transitioning to classical dynamics. This study derives the decoherence condition for quantum chaotic systems, verified using the standard map model.
Area of Science:
- Quantum Chaos
- Quantum Decoherence
- Quantum-Classical Correspondence
Background:
- Environmental interactions degrade quantum coherence.
- Decoherence can drive quantum systems towards classical behavior.
- Understanding this transition is crucial for quantum mechanics.
Purpose of the Study:
- To investigate the dynamics of quantum chaotic systems influenced by an environment.
- To derive the general condition for the transition from quantum to classical dynamics.
- To numerically validate the derived condition using a specific chaotic system.
Main Methods:
- Employed a semiclassical technique to study the decoherence process.
- Analyzed the quantum standard map on a torus as a model chaotic system.
- Performed numerical simulations to verify the theoretical findings.
Main Results:
- Obtained a general condition for the transition from quantum to classical dynamics.
- The condition was successfully verified numerically for the quantum standard map.
- The study provides insights into the mechanism of decoherence in chaotic systems.
Conclusions:
- The environment plays a critical role in the loss of quantum coherence.
- The derived condition accurately describes the quantum-to-classical transition.
- Results contribute to understanding the correspondence between quantum and classical mechanics.
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