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Spectral properties and dynamical tunneling in constant-width billiards.

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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.

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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.