Short periodic orbit approach to resonances and the fractal Weyl law

Abstract

We investigate the properties of the semiclassical short periodic orbit approach for the study of open quantum maps that was recently introduced in [M. Novaes, J.M. Pedrosa, D. Wisniacki, G.G. Carlo, and J.P. Keating, Phys. Rev. E 80, 035202(R) 2009]. We provide conclusive 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 $|{\psi }_n^R><{\psi }_n^L|$, which involves the right and left states associated with a given eigenvalue and is supported on the classical phase space repeller.

5 pages, 5 figures

References in corpus (14)

• Combining directional light output and ultralow loss in deformed microdisks
• Formation of long-lived, scarlike modes near avoided resonance crossings in optical microcavities
• Fractal Weyl laws for chaotic open systems
• Quantum-to-classical crossover of quasi-bound states in open quantum systems
• Semiclassical structure of chaotic resonance eigenfunctions
• Fractal Weyl law for quantum fractal eigenstates
• Localization of resonance eigenfunctions on quantum repellers
• Scarring by homoclinic and heteroclinic orbits
• Quantum chaotic resonances from short periodic orbits
• Fractal Weyl law behavior in an open, chaotic Hamiltonian system
• Scarring in open quantum systems
• Fractal Weyl law for three-dimensional chaotic hard-sphere scattering systems
• Distribution of resonances in the quantum open baker map
• Semi-classical Scar functions in phase space

Cited by in corpus (18)

• Leaking Chaotic Systems
• Resonances in open quantum maps
• Weyl asymptotics: From closed to open systems
• Formation and interaction of resonance chains in the open 3-disk system
• Quantum signatures of classical multifractal measures
• Using basis sets of scar functions
• Short periodic orbits theory for partially open quantum maps
• Universal intensity statistics of multifractal resonance states
• Lagrangian descriptors for open maps
• Multifractality of open quantum systems
• Classical transients and the support of open quantum maps
• Transient features of quantum open maps
• The role of short periodic orbits in quantum maps with continuous openings
• Local random vector model for semiclassical fractal structure of chaotic resonance states
• Resonance states of the three-disk scattering system
• Semiclassical Limit of Resonance States in Chaotic Scattering
• Self-Similarity Among Energy Eigenstates
• Left-Right Husimi Representation of Chaotic Resonance States: Invariance and Factorization