Statistical analysis of scars in stadium billiard
Abstract
In this paper, by using our improved plane wave decomposition method, we study the scars in the eigenfunctions of the stadium billiard from very low state to as high as about the one millionth state. In the systematic searching for scars of various types, we have used the approximate criterion based on the quantization of the classical action along the unstable periodic orbit supporting the scar. We have analized the profile of the integrated probability density along the orbit. We found that the maximal integrated intensity of different types of scars scales in different way with the , which confirms qualitatively and quantitatively the existing theories of scars such as that of Bogomolny (1988) and that of Robnik (1989).
Cite
@article{arxiv.cond-mat/9712082,
title = {Statistical analysis of scars in stadium billiard},
author = {Baowen Li and Bambi Hu},
journal= {arXiv preprint arXiv:cond-mat/9712082},
year = {2009}
}
Comments
22 plain Latex pages, 14 EPS figures (Figs. 4-6, 9,10,12 are included, others (too large) are availabe upon request.) to appear in J. Phys. A: Math. & Gen. 31 (1998)