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Closed almost-periodic orbits in semiclassical quantization of generic polygons
1Theoretical Physics Division, Bhabha Atomic Research Centre, Trombay, Mumbai, India.
Summary
Corrections to semiclassical theories are often nonclassical. However, for polygonal billiards, these corrections predominantly arise from classical closed almost-periodic (CAP) orbits, which are crucial for semiclassical quantization.
Area of Science:
- Quantum mechanics
- Classical mechanics
- Mathematical physics
Background:
- Semiclassical theories rely on periodic orbits.
- Corrections to these theories are typically nonclassical.
- The role of non-periodic orbits in semiclassical physics is not fully understood.
Purpose of the Study:
- To investigate the origin of corrections in semiclassical theories for polygonal billiards.
- To determine the contribution of different orbit families to semiclassical quantization.
- To assess the importance of closed almost-periodic (CAP) orbits.
Main Methods:
- Analysis of generic polygonal billiards.
- Identification and characterization of periodic and closed almost-periodic (CAP) orbit families.
- Comparison of the weights and prevalence of different orbit families.
Main Results:
- Corrections to semiclassical theories for polygonal billiards are predominantly classical.
- Closed almost-periodic (CAP) orbit families significantly contribute to these corrections.
- CAP orbit families are more numerous than periodic families and have comparable weights.
Conclusions:
- Closed almost-periodic (CAP) orbits are indispensable for semiclassical quantization in polygonal billiards.
- The study highlights the significant role of classical dynamics in semiclassical phenomena.
- Findings necessitate a re-evaluation of the classical versus nonclassical contributions in semiclassical theories.