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Dynamical tunneling in mushroom billiards.
A Bäcker1, R Ketzmerick, S Löck
1Institut für Theoretische Physik, Technische Universität Dresden, D-01062 Dresden, Germany.
Physical Review Letters
|June 4, 2008
Summary
We investigated dynamical tunneling in two-dimensional systems, finding agreement between experimental, numerical, and analytical methods. Our approach accurately predicts tunneling rates in billiards without needing free parameters.
Area of Science:
- Physics
- Quantum Mechanics
- Chaos Theory
Background:
- Dynamical tunneling is a quantum phenomenon where systems transition between classically separated regions.
- Understanding tunneling rates is crucial for characterizing quantum chaos in two-dimensional Hamiltonian systems.
- Previous models for billiards often required free parameters for accurate predictions.
Purpose of the Study:
- To investigate dynamical tunneling in generic two-dimensional Hamiltonian systems.
- To determine regular-to-chaotic tunneling rates.
- To validate a new analytical approach against experimental and numerical data.
Main Methods:
- Experimental investigation using microwave spectra of a mushroom billiard with adjustable foot height.
- Numerical calculation of tunneling rates from high-precision eigenvalues via the improved method of particular solutions.
- Analytical prediction by extending an approach using a fictitious integrable system to billiards.
Main Results:
- Experimental, numerical, and analytical methods were employed to study dynamical tunneling.
- Tunneling rates were obtained using microwave spectra and high-precision eigenvalues.
- A novel analytical prediction showed agreement with experimental and numerical data.
Conclusions:
- The developed analytical approach accurately predicts tunneling rates in billiards.
- This method achieves agreement without relying on any free parameters.
- The study provides a robust framework for understanding dynamical tunneling in complex systems.
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