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Weyl law for open systems with sharply divided mixed phase space

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Article number046203
<mark>Journal publication date</mark>5/04/2012
<mark>Journal</mark>Physical Review E
Issue number4
Number of pages7
Publication StatusPublished
<mark>Original language</mark>English


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 nontrivial 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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©2012 American Physical Society