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Regular-to-chaotic tunneling rates using a fictitious integrable system
A Bäcker1, R Ketzmerick, S Löck
1Institut für Theoretische Physik, Technische Universität Dresden, 01062 Dresden, Germany.
Physical Review Letters
|March 21, 2008
Summary
We developed a formula to predict dynamical tunneling rates in systems with mixed phase space. This method accurately models tunneling from regular states to chaotic regions, validated by numerical results.
Area of Science:
- Physics
- Quantum Mechanics
- Dynamical Systems
Background:
- Systems with mixed phase space exhibit both regular and chaotic dynamics.
- Understanding transitions between regular and chaotic states is crucial in physics.
- Dynamical tunneling is a key phenomenon in quantum chaos.
Purpose of the Study:
- To derive a predictive formula for dynamical tunneling rates.
- To quantify tunneling from regular states to the chaotic sea.
- To provide a theoretical framework for systems with mixed phase space.
Main Methods:
- Introduction of a fictitious integrable system to model regular dynamics.
- Development of a formula based on this fictitious system.
- Comparison of theoretical predictions with numerical simulations.
Main Results:
- A formula predicting dynamical tunneling rates was successfully derived.
- The formula shows agreement with numerical results for various kicked systems.
- The model is effective for regular states in a mixed phase space.
Conclusions:
- The proposed method accurately predicts dynamical tunneling rates.
- The fictitious integrable system provides a useful approximation for regular dynamics.
- This work offers a new tool for studying quantum chaos and mixed phase space systems.
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