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Semiclassics of the chaotic quantum-classical transition
Benjamin D Greenbaum1, Salman Habib, Kosuke Shizume
1Department of Physics, Columbia University, New York, New York 10027, USA.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|November 13, 2007
Summary
Environmental interactions drive the quantum-classical transition in chaotic systems. Noise regularizes the Wigner function and averages phase space structures, enabling classical approximations.
Area of Science:
- Quantum mechanics
- Classical mechanics
- Chaos theory
- Statistical physics
Background:
- Understanding the quantum-classical transition is fundamental in physics.
- Bounded chaotic systems with environmental interactions present unique challenges.
- Semiclassical methods bridge quantum and classical descriptions.
Purpose of the Study:
- To elucidate the physical mechanisms behind the quantum-classical transition in 1D bounded chaotic systems.
- To investigate the role of environmental interactions and noise.
- To connect semiclassical theory with measurement and open system dynamics.
Main Methods:
- Theoretical analysis of quantum-classical transition mechanisms.
- Application of measurement and open system theories.
- High-resolution numerical simulations of the quantum master equation.
- Analysis of the semiclassical Wigner function.
Main Results:
- Noise plays a dual role: regularizing the Wigner function and averaging classical phase space structures.
- A local semiclassical picture is stabilized by these mechanisms.
- The system can be approximated by a classical distribution at later times.
- Demonstrated explicitly for a chaotic Duffing oscillator.
Conclusions:
- The study clarifies the physical basis for the emergence of classical behavior from quantum chaotic systems.
- Environmental noise is crucial for regularizing quantum dynamics and enabling classical approximations.
- The findings have implications for understanding quantum measurement and open quantum systems.
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