Classification of perturbations of the hydrogen atom
by small static electric and magnetic fields
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
(Proc. R. Soc. A)
Issue Volume 463, Number 2083 / July 08, 2007
Pages 1771-1790
DOI 10.1098/rspa.2007.1843
http://www.journals.royalsoc.ac.uk/content/g44318v573v04571
Authors
K. Efstathiou
Instituut voor Wiskunde en Informatica, Rijksuniversiteit Groningen,
Groningen 9747 AC, The Netherlands
D.A. Sadovskií & B.I. Zhilinskií
UMR du CNRS 8101, Université du Littoral, 59140 Dunkerque, France
Abstract:
We consider perturbations of the hydrogen atom by sufficiently small
homogeneous static electric and magnetic fields of all possible mutual
orientations. Normalizing with regard to the Keplerian symmetry, we uncover
resonances and conjecture that the parameter space of this family of dynamical
systems is stratified into zones centred on the resonances. The 1:1 resonance
corresponds to the orthogonal field limit, studied earlier by Cushman &
Sadovskií (Cushman & Sadovskií 2000 Physica 142, 166-196). We describe the
structure of the 1:1 zone, where the system may have monodromy of different
kinds, and consider briefly the 1:2 zone.
Keywords:
perturbed Kepler system, singular reduction, energy-momentum map, monodromy