title: Chaotic spectroscopy.
abstract: 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.
authors.affiliation: 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.
authors.forename: Eyal
authors.initials: E
authors.lastname: Doron
authors.forename: Uzy
authors.initials: U
authors.lastname: Smilansky