Application of the diffraction trace formula to the three disk scattering system

The diffraction trace formula ({\em Phys. Rev. Lett.} {\bf 73}, 2304 (1994)) and spectral determinant are tested on the open three disk scattering system. The system contains a generic and exponentially growing number of diffraction periodic orbits. In spite of this it is shown that even the scattering resonances with large imaginary part can be reproduced semiclassicaly. The non-trivial interplay of the diffraction periodic orbits with the usual geometrical orbits produces the fine structure of the complicated spectrum of scattering resonances, which are beyond the resolution of the conventional periodic orbit theory.Comment: Latex article + 3 ps figure

A Fredholm Determinant for Semi-classical Quantization

We investigate a new type of approximation to quantum determinants, the ``\qFd", and test numerically the conjecture that for Axiom A hyperbolic flows such determinants have a larger domain of analyticity and better convergence than the \qS s derived from the \Gt. The conjecture is supported by numerical investigations of the 3-disk repeller, a normal-form model of a flow, and a model 2-$d$ map.Comment: Revtex, Ask for figures from [email protected]

Periodic Orbit Quantization beyond Semiclassics

A quantum generalization of the semiclassical theory of Gutzwiller is given. The new formulation leads to systematic orbit-by-orbit inclusion of higher $\hbar$ contributions to the spectral determinant. We apply the theory to billiard systems, and compare the periodic orbit quantization including the first $\hbar$ contribution to the exact quantum mechanical results.Comment: revte