Quantitative study of scars in the boundary section of the stadium billiard

Details Quantitative study of scars in the boundary section of the stadium billiard Quantitative study of scars in the boundary section of the stadium billiard

1997-06-24

arxiv.org/abs/chao-dyn/9706024v1

Nonlinear Sciences

Chaotic Dynamics

10 pages, RevTex, 14 Figures (10 gifs, 4 PostScripts). Submitted to Physical Review E

Scientific paper

10.1103/PhysRevE.56.3859

We construct a semiclassically invariant function on the boundary of the billiard, taken as the Poincare section in Birkhoff coordinates, based on periodic orbit information, as an ansatz for the normal derivative of the eigenfunction. Defining an appropriate scalar product on the section, we can compute the scar intensity of a given periodic orbit on an eigensate, as the overlap beetween the constructed function and the normal derivative on the section of the eigenstate. In this way, we are able to investigate how periodic orbits scar the spectrum and how a given eigenstate decompose into scar functions. We use this scheme on the Bunimovich stadium.

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