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Journal
2012 | 10 | 4 | 742-748
Article title

C1 non-integrability of a hydrogen atom in a circularly polarized microwave field

Content
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Languages of publication
EN
Abstracts
EN
Barrabés et al. [Physica D, 241(4), 333–349, 2012] consider the problem of the hydrogen atom interacting with a circularly polarized microwave field modeled as a planar perturbed Kepler problem. For different values of the parameter, the authors offer some numerical evidence of the non-integrability of this problem. The objective of the present work is to give an analytical proof of the C1 non-integrability of this problem for any value of the parameter using the averaging theory as a main tool.
Publisher
Journal
Year
Volume
10
Issue
4
Pages
742-748
Physical description
Dates
published
1 - 8 - 2012
online
17 - 7 - 2012
References
  • [1] E. Barrabés, M. Ollé, F. Borondo, D. Farrelly, J. Mondelo, Physica D 241, 333 (2012) http://dx.doi.org/10.1016/j.physd.2011.10.016[Crossref]
  • [2] R. Abraham, J. E. Marsden, Foundations of Mechanics, (Benjamin, Reading, Masachusets, 1978)
  • [3] V. I. Arnold, V. Kozlov, A. Neishtadt, Dynamical Systems III. Mathematical Aspects of Classical and Celestial Mechanics, Third Edition, Encyclopaedia of Mathematical Science, (Springer, Berlin, 2006)
  • [4] A. Deprit, Celest. Mech. Dyn. Ast. 51, 201 (1991) http://dx.doi.org/10.1007/BF00051691[Crossref]
  • [5] H. Poincaré, Les méthodes nouvelles de la mécanique céleste, Vol. I, (Gauthier-Villars, Paris 1899)
  • [6] F. Verhulst, Nonlinear Differential Equations and Dynamical Systems, (Universitext, Springer, 1991)
  • [7] E. T. Whittaker, A Treatise on the Analytical Dynamics of Particles and Rigid Bodies, Cambridge Mathematical Library, (Cambridge University Press, 1989)
Document Type
Publication order reference
YADDA identifier
bwmeta1.element.-psjd-doi-10_2478_s11534-012-0077-0
Identifiers
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