Statistical analysis of scars in stadium billiard

Details Statistical analysis of scars in stadium billiard Statistical analysis of scars in stadium billiard

1997-12-06

arxiv.org/abs/cond-mat/9712082v1

Physics

Condensed Matter

Statistical Mechanics

22 plain Latex pages, 14 EPS figures (Figs. 4-6, 9,10,12 are included, others (too large) are availabe upon request.) to appea

Scientific paper

10.1088/0305-4470/31/2/010

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 $\hbar$, which confirms qualitatively and quantitatively the existing theories of scars such as that of Bogomolny (1988) and that of Robnik (1989).

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