Chaotic spectroscopy.
The spectra of quantized chaotic billiards from the point of view of scattering theory are discussed. It is shown how the spectral and resonance density functions both fluctuate about a common mean. A semiclassical treatment explains this in terms of classical scattering trajectories and periodic orbits of the Poincare scattering map. It is shown that this formalism provides an alternative derivation and a new interpretation of Gutzwiller's periodic orbits sum for the spectral density. Moreover, it is a convenient starting point for a derivation of a Riemann-Siegel "look alike" expression for the secular equation in terms of periodic orbits of finite length.
Doron
Eyal
E
Department of Nuclear Physics, The Weizmann Institute of Science, Rehovot 76100, IsraelH. H. Wills Physics Laboratory, Royal Fort, Tyndall Avenue, Bristol BS8 1TL, United Kingdom.
Smilansky
Uzy
U