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Spectral properties and dynamical tunneling in constant-width billiards.
1Institut für Kernphysik, Technische Universität Darmstadt, D-64289 Darmstadt, Germany.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|September 13, 2014
Summary
Quantum billiards exhibit dynamical tunneling, allowing motion changes via quantum effects. Resonance spectra reveal this through split energy levels, matching random-matrix theory predictions for mixed chaotic systems.
Area of Science:
- Quantum mechanics
- Chaos theory
- Spectroscopy
Background:
- Classical billiards exhibit unidirectional motion.
- Quantum systems can exhibit dynamical tunneling, enabling motion direction changes.
- Resonance spectra provide insights into quantum system dynamics.
Purpose of the Study:
- To accurately determine low-lying eigenvalues of quantum billiards.
- To investigate dynamical tunneling in quantum systems.
- To analyze resonance splitting and its relation to random-matrix models.
Main Methods:
- Measurement of resonance spectra using superconducting microwave resonators.
- Analysis of quantum billiard eigenvalues.
- Application of random-matrix theory for spectral analysis.
Main Results:
- Accurate determination of 900 lowest eigenvalues for two quantum billiards.
- Observation of resonance splitting due to dynamical tunneling.
- Fluctuation properties of spectra match random-matrix models for violated time-reversal invariance and mixed dynamics.
Conclusions:
- Dynamical tunneling is a key quantum phenomenon in these billiards.
- Resonance splitting serves as a signature of tunneling.
- A derived analytical expression for splitting distribution is applicable to systems with dynamical tunneling and chaotic dynamics.
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