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arXiv · 1203.4462

Weyl law for open systems with sharply divided mixed phase space

Akihiro Ishii·Akira Akaishi·Akira Shudo·Henning Schomerus
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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.

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Akihiro Ishii, Akira Akaishi, Akira Shudo, Henning Schomerus. 2012-04-04. Weyl law for open systems with sharply divided mixed phase space. https://doi.org/10.1103/physreve.85.046203

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