scholarly journals self-similarity of Rydberg hydrogen atom in parallel electric and magnetic fields

2015 ◽  
Vol 64 (18) ◽  
pp. 180502
Author(s):  
Li Hong-Yun ◽  
Yin Yan-Yan ◽  
Wang Qing ◽  
Wang Li-Fei
Keyword(s):  
Hydrogen Atom ◽  
Magnetic Fields ◽  
Self Similarity ◽  
Electric And Magnetic Fields ◽  
Rydberg Hydrogen Atom

scholarly journals Classification of perturbations of the hydrogen atom by small static electric and magnetic fields

2007 ◽  
Vol 463 (2083) ◽  
pp. 1771-1790 ◽  
Author(s):  
K Efstathiou ◽  
D.A Sadovskií ◽  
B.I Zhilinskií
Keyword(s):  
Dynamical Systems ◽  
Hydrogen Atom ◽  
Magnetic Fields ◽  
Parameter Space ◽  
Field Limit ◽  
Electric And Magnetic Fields ◽  
Orthogonal Field

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.

scholarly journals A Surface of Section for Hydrogen in Crossed Electric and Magnetic Fields

Mathematics ◽  
2018 ◽  
Vol 6 (10) ◽  
pp. 185
Author(s):  
Korana Burke ◽  
Kevin Mitchell
Keyword(s):  
Nonlinear Dynamics ◽  
Dynamical Systems ◽  
Hydrogen Atom ◽  
Magnetic Fields ◽  
Geometric Approach ◽  
Electron Dynamics ◽  
Surface Of Section ◽  
Electric And Magnetic Fields ◽  
Global Surface ◽  
Global Surface Of Section

A well defined global surface of section (SOS) is a necessary first step in many studies of various dynamical systems. Starting with a surface of section, one is able to more easily find periodic orbits as well as other geometric structures that govern the nonlinear dynamics of the system in question. In some cases, a global surface of section is relatively easily defined, but in other cases the definition is not trivial, and may not even exist. This is the case for the electron dynamics of a hydrogen atom in crossed electric and magnetic fields. In this paper, we demonstrate how one can define a surface of section and associated return map that may fail to be globally well defined, but for which the dynamics is well defined and continuous over a region that is sufficiently large to include the heteroclinic tangle and thus offers a sound geometric approach to studying the nonlinear dynamics.

Periodic-orbit spectroscopy of the hydrogen atom in parallel electric and magnetic fields

1994 ◽  
Vol 49 (4) ◽  
pp. 2734-2747 ◽  
Author(s):  
M. A. Iken ◽  
F. Borondo ◽  
R. M. Benito ◽  
T. Uzer
Keyword(s):  
Hydrogen Atom ◽  
Magnetic Fields ◽  
Periodic Orbit ◽  
Electric And Magnetic Fields
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