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Classical invariants and the quantization of chaotic systems.
D A Wisniacki1, E Vergini, R M Benito
1Departamento de Química C-IX, Universidad Autónoma de Madrid, Cantoblanco, 28049 Madrid, Spain.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|November 5, 2004
Summary
Long periodic orbits hinder Gutzwiller
Area of Science:
- Quantum mechanics and chaos theory
- Classical and semiclassical dynamics
Background:
- Gutzwiller's theory for chaotic systems relies on periodic orbits.
- The exponential proliferation of long periodic orbits poses a significant challenge.
- This limits the application of semiclassical quantization schemes.
Purpose of the Study:
- To explore alternative classical invariants for semiclassical quantization.
- To address the limitations of using long periodic orbits in chaotic systems.
- To investigate dynamical analysis of chaotic quantum spectra.
Main Methods:
- Dynamical analysis of chaotic quantum spectra.
- Identification of classical invariant areas.
- Focus on stable and unstable manifolds of short periodic orbits.
Main Results:
- Classical invariant areas associated with short periodic orbits are relevant.
- These invariant areas offer a potential alternative to long periodic orbits.
- The dynamical analysis successfully unveiled the role of these areas.
Conclusions:
- Classical invariant areas related to short periodic orbits can be used in semiclassical quantization.
- This approach circumvents the problem of long periodic orbit proliferation.
- Offers a promising direction for studying chaotic quantum systems.