Weyl law for fat fractals
arXiv:1007.2819 · doi:10.1088/1751-8113/43/39/392003
Abstract
It has been conjectured that for a class of piecewise linear maps the closure of the set of images of the discontinuity has the structure of a fat fractal, that is, a fractal with positive measure. An example of such maps is the sawtooth map in the elliptic regime. In this work we analyze this problem quantum mechanically in the semiclassical regime. We find that the fraction of states localized on the unstable set satisfies a modified fractal Weyl law, where the exponent is given by the exterior dimension of the fat fractal.
arXiv comment8 pages, 4 figures, IOP format
References in corpus (8)
- Fractal Weyl laws for chaotic open systems
- Quantum-to-classical crossover of quasi-bound states in open quantum systems
- Fractal Weyl laws in discrete models of chaotic scattering
- Fractal Weyl law for quantum fractal eigenstates
- Hamiltonian mappings and circle packing phase spaces
- Weyl's law and quantum ergodicity for maps with divided phase space
- Fractal Weyl laws for quantum decay in generic dynamical systems
- Hamiltonian mappings and circle packing phase spaces: numerical investigations