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Weyl law for open systems with sharply divided mixed phase space.

Authors
  • Ishii, Akihiro
  • Akaishi, Akira
  • Shudo, Akira
  • Schomerus, Henning
Type
Published Article
Journal
Physical Review E
Publisher
American Physical Society (APS)
Publication Date
Apr 01, 2012
Volume
85
Issue
4 Pt 2
Pages
46203–46203
Identifiers
PMID: 22680552
Source
Medline
License
Unknown

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 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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