Numerical study of scars in a chaotic billiard

Abstract

We study numerically the scaling properties of scars in stadium billiard. Using the semiclassical criterion, we have searched systematically the scars of the same type through a very wide range, from ground state to as high as the 1 millionth state. We have analyzed the integrated probability density along the periodic orbit. The numerical results confirm that the average intensity of certain types of scars is independent of $\hslash$ rather than scales with $\sqrt{\hslash }$. Our findings confirm the theoretical predictions of Robnik (1989).

7 pages in Revtex 3.1, 5 PS figures available upon request. To appear in Phys. Rev. E, Vol. 55, No. 5, 1997

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• Statistical analysis of scars in stadium billiard
• Relevance of Chaos in Numerical Solutions of Quantum Billiards
• Correlations of chaotic eigenfunctions: a semiclassical analysis
• Numerical accuracy of Bogomolny's semiclassical quantization scheme in quantum billiards