Complete classification of qualitatively different perturbations of the hydrogen atom in weak near-orthogonal electric and magnetic fields

Abstract

We consider perturbations of the hydrogen atom by sufficiently small homogeneous static electric and magnetic fields in near-orthogonal configurations. Normalization of the Keplerian symmetry reveals that in the parameter space such systems belong in a ‘zone’ of systems close to the 1:1 resonance, the latter corresponding to the exactly orthogonal configuration. Integrable approximations obtained from second normalization of systems in the 1:1 zone are classified into several different qualitative types, many of which possess nontrivial monodromy. We compute monodromy of the complete three-dimensional energy–momentum map, compare the joint quantum spectrum to classical bifurcation diagrams, and show the effect of second normalization to the joint spectrum.