Weyl law for open systems with sharply divided mixed phase space
arXiv:1203.4462 · doi:10.1103/PhysRevE.85.046203
Abstract
A generalization of the Weyl law to systems with a sharply divided mixed phase space is proposed. The ansatz is composed of the usual Weyl term which counts the number of states in regular islands and a term associated with sticky regions in phase space. For a piecewise linear map, we numerically check the validity of our hypothesis, and find good agreement not only for the case with a sharply divided phase space, but also for the case where tiny island chains surround the main regular island. For the latter case, a non-trivial power law exponent appears in the survival probability of classical escaping orbits, which may provide a clue to develop the Weyl law for more generic mixed systems.
8 pages, 14 figures
References in corpus (9)
- Long-Time Correlations in the Stochastic Regime
- Fractal Weyl laws for chaotic open systems
- Quantum-to-classical crossover of quasi-bound states in open quantum systems
- Fractal Weyl law for chaotic microcavities: Fresnel's laws imply multifractal scattering
- Fractal Weyl law for quantum fractal eigenstates
- Fractal Weyl law for three-dimensional chaotic hard-sphere scattering systems
- Distribution of resonances in the quantum open baker map
- Partial Weyl Law for Billiards
- Weyl law for fat fractals