Short periodic orbit approach to resonances and the fractal Weyl law

M. NOVAES, J. M. PEDROSA, D. WISNIACKI, G. G. CARLO

PHYSICAL REVIEW E - STATISTICAL PHYSICS, PLASMAS, FLUIDS AND RELATED INTERDISCIPLINARY TOPICS

APS

Año: 2012 vol. 85 p. 362031 - 362034

1063-651X

We investigate the properties of the semiclassical short periodic orbit approach for the study of open quantum maps that was recently introduced [ Novaes, Pedrosa, Wisniacki, Carlo and Keating Phys. Rev. E 80 035202 (2009)]. We provide solid numerical evidence, for the paradigmatic systems of the open baker and cat maps, that by using this approach the dimensionality of the eigenvalue problem is reduced according to the fractal Weyl law. The method also reproduces the projectors |ψnR〉〈ψnL|, which involves the right and left states associated with a given eigenvalue and is supported on the classical phase-space repeller.