Document Type
Article
Department/Program
Physics
Journal Title
Physical Review A
Pub Date
2-1992
Publisher
American Physical Society
Volume
45
Issue
3
First Page
1746
Abstract
Classically chaotic systems possess a proliferation of periodic orbits. This phenomenon was observed in a quantum system through measurements of the absorption spectrum of a hydrogen atom in a magnetic field. This paper gives a theoretical interpretation of the bifurcations of periodic or closed orbits of electrons in atoms in magnetic fields. We ask how new periodic orbits can be created out of existing ones or ‘‘out of nowhere’’ as the energy changes. Hamiltonian bifurcation theory provides the answer: it asserts the existence of just five typical types of bifurcation in conservative systems with two degrees of freedom. We show an example of each type. Every case we have examined falls into one of the patterns described by the theory.
Recommended Citation
Mao, J. M. and Delos, John B., Hamiltonian Bifurcation Theory of Closed Orbits in the Diamagnetic Kepler Problem (1992). Physical Review A, 45(3), 1746-1761.
https://doi.org/10.1103/PhysRevA.45.1746
DOI
https://doi.org/10.1103/PhysRevA.45.1746
