Semiclassical criterion for scars in wave functions of chaotic systems
- 8 August 1994
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review Letters
- Vol. 73 (6) , 806-809
- https://doi.org/10.1103/physrevlett.73.806
Abstract
A semiclassical criterion for the existence of scars, formulated in terms of a finite number of classical periodic orbits, is shown to be useful in order to predict scarring of specific wave functions of chaotic systems, and to partly disentangle their structure. This is demonstrated by a numerical study of wave functions of a chaotic billiard that are of sufficiently high energy to be considered semiclassical.Keywords
This publication has 21 references indexed in Scilit:
- Semiclassical quantization of chaotic billiards: a scattering theory approachNonlinearity, 1992
- Experimental determination of billiard wave functionsPhysical Review Letters, 1992
- A new asymptotic representation for ζ(½ + i t ) and quantum spectral determinantsProceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences, 1992
- Quantum scars of classical closed orbits in phase spaceProceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 1989
- Quantum mechanics of a classically chaotic system: Observations on scars, periodic orbits, and vibrational adiabaticityPhysical Review A, 1989
- Ergodicit et fonctions propres du laplacienCommunications in Mathematical Physics, 1985
- Bound-State Eigenfunctions of Classically Chaotic Hamiltonian Systems: Scars of Periodic OrbitsPhysical Review Letters, 1984
- Regular and irregular semiclassical wavefunctionsJournal of Physics A: General Physics, 1977
- 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