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

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)

References in corpus (1)

• Numerical study of scars in a chaotic billiard

Cited by in corpus (9)

• Recent Developments in the Theory of Scarring
• Measuring Scars of Periodic Orbits
• Localization of Eigenfunctions in the Stadium Billiard
• Chaotic eigenfunctions in momentum space
• Exact distribution of spacing ratios for random and localized states in quantum chaotic systems
• Relevance of Chaos in Numerical Solutions of Quantum Billiards
• Can billiard eigenstates be approximated by superpositions of plane waves?
• Correlations of chaotic eigenfunctions: a semiclassical analysis
• Numerical accuracy of Bogomolny's semiclassical quantization scheme in quantum billiards