Eigenfunctions of Bunimovich billiard in coherent state representation

by Fernando P. Simonotti


We study the semiclassical limit of eigenfunctions of classicaly chaotic systems.
Particularly, we focus our analysis on the scarring phenomenon, in which the
probability density shows spectacular enhancements along periodic orbits of the
underlying classical system. We develop to this effect a method for detecting
scars in the quantum spectrum. Using this construction on the stadium billiard,
we are able, by means of symbolic dynamics, to identify scars of single periodic
orbits and of families of them in the spectrum.
Moreover, we are able to obtain a semiclassical expression for the projector
onto eigenfunctions bt means of the Fredholm theory. We express the projector
in the coherent state basis, thus obtaining the semiclassical Husimi
representation of the stadium eigenfunctions, which is written in terms of
classical invariants: periodic points, their monodromy matrices and Maslov

Keywords: quantum chaos, semiclassical limit, Fredholm methods, scars, Bunimovich stadium.

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