Semiclassical level spacings when regular and chaotic orbits coexist
- 21 August 1984
- journal article
- Published by IOP Publishing in Journal of Physics A: General Physics
- Vol. 17 (12), 2413-2421
- https://doi.org/10.1088/0305-4470/17/12/013
Abstract
The authors calculate semiclassical limiting level spacing distributions P(S) for systems whose classical energy surface is divided into a number of separate region in which motion is regular or chaotic. In the calculation it is assumed that the spectrum is the superposition of statistically independent sequences of levels from each of the classical phase-space regions, sequences from regular regions, having Poisson distributions and those from irregular regions having Wigner distributions. The formulae for P(S) depend on the sum of the Liouville measures of all the classical regular regions, and on the separate Liouville measures of the significant chaotic regions.Keywords
This publication has 18 references indexed in Scilit:
- The adiabatic limit and the semiclassical limitJournal of Physics A: General Physics, 1984
- Characterization of Chaotic Quantum Spectra and Universality of Level Fluctuation LawsPhysical Review Letters, 1984
- Regularity and chaos in classical mechanics, illustrated by three deformations of a circular 'billiard'European Journal of Physics, 1981
- Quantizing a classically ergodic system: Sinai's billiard and the KKR methodAnnals of Physics, 1981
- On the connection between quantization of nonintegrable systems and statistical theory of spectraLettere al Nuovo Cimento (1971-1985), 1980
- Level clustering in the regular spectrumProceedings of the Royal Society of London. Series A - Mathematical and Physical Sciences, 1977
- Distribution of eigenfrequencies for the wave equation in a finite domain: III. Eigenfrequency density oscillationsAnnals of Physics, 1972
- Phase-Integral Approximation in Momentum Space and the Bound States of an Atom. IIJournal of Mathematical Physics, 1969
- Phase-Integral Approximation in Momentum Space and the Bound States of an AtomJournal of Mathematical Physics, 1967
- Repulsion of nuclear levelsNuclear Physics, 1957