Periodic-orbit quantization of chaotic systems.

We demonstrate the utility of the periodic-orbit description of chaotic motion by computing from a few periodic orbits highly accurate estimates of a large number of quantum resonances for the classically chaotic three-disk scattering problem. The symmetry decompositions of the eigenspectra are the same for the classical and the quantum problem, and good agreement between the periodic-orbit estimates and the exact quantum poles is observed

[1]  Cvitanovic,et al.  Invariant measurement of strange sets in terms of cycles. , 1988, Physical review letters.

[2]  A. Voros.  Unstable periodic orbits and semiclassical quantisation , 1988 .

[3]  E. Aurell,et al.  Convergence of the Semi-Classical Periodic Orbit Expansion , 1989 .

[4]  B. Eckhardt.  Fractal properties of scattering singularities , 1987 .

[5]  A. Mullin,et al.  Group Theory and its Applications to Physical Problems , 1962 .

[6]  S. Rice,et al.  Semiclassical quantization of the scattering from a classically chaotic repellor , 1989 .

[7]  M. Gutzwiller.  From classical to quantum mechanics with hard chaos , 1988 .

[8]  L. Kadanoff,et al.  Escape from strange repellers. , 1984, Proceedings of the National Academy of Sciences of the United States of America.

[9]  M. Gutzwiller,et al.  Energy Spectrum According to Classical Mechanics , 1970 .

[10]  R. Balian,et al.  Solution of the Schrodinger Equation in Terms of Classical Paths , 1974 .

[11]  M. Hamermesh.  Group theory and its application to physical problems , 1962 .

[12]  M. Gutzwiller.  Phase-Integral Approximation in Momentum Space and the Bound States of an Atom , 1967 .

[13]  David Ruelle,et al.  Thermodynamic Formalism: The Mathematical Structures of Classical Equilibrium Statistical Mechanics , 1978 .

[14]  M. Gutzwiller,et al.  Periodic Orbits and Classical Quantization Conditions , 1971 .

[15]  D. Ruelle.  Locating resonances for AxiomA dynamical systems , 1986 .

[16]  S. Rice,et al.  Scattering from a classically chaotic repellor , 1989 .

[17]  W. Parry,et al.  An analogue of the prime number theorem for closed orbits of Axiom A flows , 1983 .

[18]  S. Rice,et al.  Exact quantization of the scattering from a classically chaotic repellor , 1989 .