Singular continuous spectra in a pseudo-integrable billiard

Abstract

The pseudo-integrable barrier billiard invented by Hannay and McCraw [J. Phys. A 23, 887 (1990)] -- rectangular billiard with line-segment barrier placed on a symmetry axis -- is generalized. It is proven that the flow on invariant surfaces of genus two exhibits a singular continuous spectral component.

4 pages, 2 figures

References in corpus (1)

• Mixing property of triangular billiards

Cited by in corpus (8)

• Hexagonal dielectric resonators and microcrystal lasers
• Fractal Weyl law for chaotic microcavities: Fresnel's laws imply multifractal scattering
• Spectral properties of quantized barrier billiards
• Two scenarios for quantum multifractality breakdown
• The Quantum-Classical Correspondence in Polygonal Billiards
• A pseudointegrable Andreev billiard
• Multifractality of quantum wave functions in the presence of perturbations
• A sufficient condition for pseudointegrable systems with weak mixing property