1988/08/01 by R. Aurich, Martin Sieber, Frank Steiner · 1 citation
Physics and Astronomy · Mathematics · #Quantum chaos and dynamical systems #Scientific Research and Discoveries #Chaos control and synchronization #Hadamard transform #Quantum chaos #Quantization (signal processing) #Physics #Quantum #Quantum mechanics #Bohr model #Chaotic #Classical mechanics #Theoretical physics #Statistical physics #Quantum dynamics #Mathematics #Computer science
paper · doi:10.1103/physrevlett.61.483
openalex publication_date 1988/08/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/02
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.