Circular quantum billiard with a singular magnetic flux line
- 1 January 1996
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review A
- Vol. 53 (1) , 39-48
- https://doi.org/10.1103/physreva.53.39
Abstract
We discuss the application of Gutzwiller’s semiclassical theory to a circular billiard with a singular magnetic flux line added at its center. The Aharonov-Bohm effect manifests itself through the cancellation of periodic orbits for particular flux strengths. Diffraction phenomena affect the gross-shell structure of the level density and require corrections of higher order in ħ. The full quantization of the level spectrum, however, is much less affected. © 1996 The American Physical Society.Keywords
This publication has 31 references indexed in Scilit:
- Rectangular billiard in the presence of a flux linePhysical Review E, 1995
- Semiclassical accuracy for billiardsNonlinearity, 1994
- ħ expansion for the periodic-orbit quantization of hyperbolic systemsPhysical Review A, 1993
- The semiclassical helium atomChaos: An Interdisciplinary Journal of Nonlinear Science, 1992
- Validity of the semiclassical periodic orbit approximation in the two‐ and three‐disk problemsChaos: An Interdisciplinary Journal of Nonlinear Science, 1992
- Semiclassical trace formulas in the presence of continuous symmetriesPhysical Review A, 1991
- Fractal properties of scattering singularitiesJournal of Physics A: General Physics, 1987
- Statistics of energy levels without time-reversal symmetry: Aharonov-Bohm chaotic billiardsJournal of Physics A: General Physics, 1986
- Phase-Integral Approximation in Momentum Space and the Bound States of an Atom. IIJournal of Mathematical Physics, 1969
- Corrected bohr-sommerfeld quantum conditions for nonseparable systemsAnnals of Physics, 1958