Transition from Regular to Irregular Spectra in Quantum Billiards
- 15 April 1985
- journal article
- Published by American Physical Society (APS) in Physical Review Letters
- Vol. 54 (15), 1617-1619
- https://doi.org/10.1103/physrevlett.54.1617
Abstract
Statistics of energy spectra are studied for quantum billiards, i.e., free motion of a particle in two dimensions surrounded by a hard wall. The transition from regular to irregular spectra observed in moments of nearest-neighbor spacing distributions for different shapes of the boundary is analyzed by a superposition of independent level sequences with Poisson and Wigner distributions. The rate of mixture of the two sequences is compared with the rate of phase volumes spanned by quasiperiodic and chaotic orbits of the corresponding classical motion.Keywords
This publication has 13 references indexed in Scilit:
- Uncovering the Transition from Regularity to Irregularity in a Quantum SystemPhysical Review Letters, 1984
- New representation of quantum chaosPhysics Letters A, 1984
- Characterization of Chaotic Quantum Spectra and Universality of Level Fluctuation LawsPhysical Review Letters, 1984
- Quantizing a classically ergodic system: Sinai's billiard and the KKR methodAnnals of Physics, 1981
- Spectrum and Eigenfunctions for a Hamiltonian with Stochastic TrajectoriesPhysical Review Letters, 1979
- On ergodic properties of certain billiardsFunctional Analysis and Its Applications, 1975
- Regular and irregular spectraJournal of Physics B: Atomic and Molecular Physics, 1973
- Dynamical systems with elastic reflectionsRussian Mathematical Surveys, 1970
- "Repulsion of Energy Levels" in Complex Atomic SpectraPhysical Review B, 1960
- Repulsion of nuclear levelsNuclear Physics, 1957