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Fractal Weyl laws for chaotic open systems
W T Lu1, S Sridhar, Maciej Zworski
1Department of Physics and Electronic Materials Research Institute, Northeastern University, Boston, Massachusetts 02115, USA.
Physical Review Letters
|November 13, 2003
Summary
We propose a new conjecture linking quantum resonance density in open chaotic systems to the fractal dimension of classical repellers. This finding extends the Weyl law to chaotic open systems, supported by mathematical arguments and numerical simulations.
Area of Science:
- Quantum chaos
- Statistical physics
- Dynamical systems
Background:
- Open chaotic systems exhibit complex dynamics.
- Understanding quantum resonance density is crucial for characterizing these systems.
- The Weyl law describes state density in closed systems.
Purpose of the Study:
- To propose and justify a conjecture relating quantum resonance density to classical repeller fractal dimension in open chaotic systems.
- To generalize the Weyl law to open chaotic systems.
Main Methods:
- Mathematical analysis to justify the conjecture.
- Numerical computation of resonances for systems of n disks on a plane.
Main Results:
- A conjecture is presented connecting quantum resonance density to the fractal dimension of the classical repeller.
- Mathematical arguments supporting the conjecture are discussed.
- Numerical evidence from n-disk systems supports the conjecture.
Conclusions:
- The proposed conjecture provides a new link between quantum and classical properties of open chaotic systems.
- The study generalizes the Weyl law to the domain of chaotic open systems.