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
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- Counting statistics of chaotic resonances at optical frequencies: theory and experiments
- Weyl law for contractive maps