Periodic orbit quantization of the anisotropic Kepler problem
- 1 January 1992
- journal article
- conference paper
- Published by AIP Publishing in Chaos: An Interdisciplinary Journal of Nonlinear Science
- Vol. 2 (1) , 61-69
- https://doi.org/10.1063/1.165899
Abstract
The periodic orbit quantization on the anisotropic Kepler problem is tested. By computing the stability and action of some 2000 of the shortest periodic orbits, the eigenvalue spectrum of the anisotropic Kepler problem is calculated. The aim is to test the following claims for calculating the quantum spectrum of classically chaotic systems: (1) Curvature expansions of quantum mechanical zeta functions offer the best semiclassical estimates; (2) the real part of the cycle expansions of quantum mechanical zeta functions cut at appropriate cycle length offer the best estimates; (3) cycle expansions are superfluous; and (4) only a small subset of cycles (irreducible cycles) suffices for good estimates for the eigenvalues. No evidence is found to support any of the four claims.Keywords
This publication has 20 references indexed in Scilit:
- Quantization of chaotic systemsChaos: An Interdisciplinary Journal of Nonlinear Science, 1992
- Existence of stable orbits in thepotentialPhysical Review Letters, 1990
- A rule for quantizing chaos?Journal of Physics A: General Physics, 1990
- Recycling of strange sets: II. ApplicationsNonlinearity, 1990
- Recycling of strange sets: I. Cycle expansionsNonlinearity, 1990
- Unstable periodic orbits and semiclassical quantisationJournal of Physics A: General Physics, 1988
- Efficient quantisation scheme for the anisotropic Kepler problemJournal of Physics A: General Physics, 1987
- Exponential instability of collision orbit in the anisotropic Kepler problemCelestial Mechanics and Dynamical Astronomy, 1987
- Nonregularizability of the anisotropic Kepler problemJournal of Differential Equations, 1978
- Cyclotron Resonance in Uniaxially Stressed Silicon. II. Nature of the Covalent BondPhysical Review B, 1965