Rights statement: ©2012 American Physical Society
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Research output: Contribution to Journal/Magazine › Journal article › peer-review
Research output: Contribution to Journal/Magazine › Journal article › peer-review
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TY - JOUR
T1 - Weyl law for open systems with sharply divided mixed phase space
AU - Ishii, Akihiro
AU - Akaishi, Akira
AU - Shudo, Akira
AU - Schomerus, Henning
N1 - ©2012 American Physical Society
PY - 2012/4/5
Y1 - 2012/4/5
N2 - 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.
AB - 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.
U2 - 10.1103/PhysRevE.85.046203
DO - 10.1103/PhysRevE.85.046203
M3 - Journal article
VL - 85
JO - Physical Review E
JF - Physical Review E
SN - 1539-3755
IS - 4
M1 - 046203
ER -