Periodic Orbit Quantization by Harmonic Inversion of Gutzwiller's Recurrence Function

Abstract

Semiclassical eigenenergies and resonances are obtained from classical periodic orbits by harmonic inversion of Gutzwiller's semiclassical recurrence function, i.e., the trace of the propagator. Applications to the chaotic three disk scattering system and, as a mathematical model, to the Riemann zeta function demonstrate the power of the technique. The method does not depend on the existence of a symbolic code and might be a tool for a semiclassical quantization of systems with nonhyperbolic or mixed regular-chaotic dynamics as well.