Ishii Akihiro, Akaishi Akira, Shudo Akira, Schomerus Henning
Department of Physics, Tokyo Metropolitan University, Minami-Osawa, Hachioji, Tokyo, Japan.
Phys Rev E Stat Nonlin Soft Matter Phys. 2012 Apr;85(4 Pt 2):046203. doi: 10.1103/PhysRevE.85.046203. Epub 2012 Apr 5.
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.
