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

Abstract

We construct a semiclassically invariant function on the boundary of the billiard, taken as the Poincaré 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 eigenstate, as the overlap between 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 decomposes into scar functions. We use this scheme on the Bunimovich stadium. ͓S1063-651X͑97͒11509-4͔

Fredholm methods for billiard eigenfunctions in the coherent state representation

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