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Updated: Jun 29, 2026
06:42
Generation and Coherent Control of Pulsed Quantum Frequency Combs
Published on: June 8, 2018
Localized perturbations of integrable quantum billiards
1Department of Physics, Technion, Haifa 32000, Israel.
Summary
Investigating a perturbed rectangular billiard reveals distinct energy level statistics based on scatterer position. Central perturbations exhibit unique symmetries and angular dependencies, impacting energy correlations.
Area of Science:
- Quantum mechanics
- Mathematical physics
- Condensed matter physics
Background:
- Studying quantum billiards provides insights into complex systems.
- Localized potentials introduce unique behaviors in confined systems.
- Understanding energy level statistics is crucial for characterizing quantum systems.
Purpose of the Study:
- To analyze the energy level statistics of a rectangular billiard with a strong localized potential.
- To compare the effects of perturbations at the center versus a typical position.
- To investigate the role of symmetry and potential angular dependence.
Main Methods:
- Analytical calculations of energy level statistics.
- Numerical simulations of the perturbed billiard system.
- Application of the semiclassical geometrical theory of diffraction.
Main Results:
- Distinct statistical properties arise depending on scatterer location (center vs. typical).
- Central perturbations show symmetry-enhanced contributions, including angular dependence.
- The delta-like scatterer limit is explicitly derived.
- Form factors, derived from energy-energy correlations, are calculated.
- Nondiagonal classical orbit contributions are identified as essential.
Conclusions:
- Perturbation position significantly alters energy level statistics in quantum billiards.
- Symmetry plays a key role in central perturbation effects.
- The study validates analytical and numerical approaches for complex quantum systems.
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