Fractal Weyl law for three-dimensional chaotic hard-sphere scattering systems

Details Fractal Weyl law for three-dimensional chaotic hard-sphere scattering systems Fractal Weyl law for three-dimensional chaotic hard-sphere scattering systems

2010-08-04

arxiv.org/abs/1008.0718v1

Phys. Rev. E 82, 046201 (2010)

Nonlinear Sciences

Chaotic Dynamics

12 pages, 8 figures, submitted to Phys. Rev. E

Scientific paper

10.1103/PhysRevE.82.046201

The fractal Weyl law connects the asymptotic level number with the fractal dimension of the chaotic repeller. We provide the first test for the fractal Weyl law for a three-dimensional open scattering system. For the four-sphere billiard, we investigate the chaotic repeller and discuss the semiclassical quantization of the system by the method of cycle expansion with symmetry decomposition. We test the fractal Weyl law for various symmetry subspaces and sphere-to-sphere separations.

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