Quantum Chaos of the Hadamard-Gutzwiller Model

We present a theory of quantum chaos of the Hadamard-Gutzwiller model, a quantum mechanical system which describes the motion of a particle on a surface of constant negative curvature. The theory is based on periodic-orbit sum rules that can be rigorously derived from the Selberg trace formula and which provide an exact substitute, appropriate for our strongly chaotic system, for the Bohr-Sommerfeld-Einstein quantization rules. Our recent enumeration of the classical periodic orbits enables us to evaluate the sum rules numerically and to demonstrate thereby that the theory provides also a practical method to study the quantum chaos of spectra.