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

• Authors: Juan Guirao , Miguel López , Juan Vera
• 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.

Keywords

EN

Hamiltonian system; perturbed Kepler problem; integrability; averaging theory

• Publisher: De Gruyter Open
• Journal: Open Physics
• Year: 2012
• Volume: 10
• Issue: 4
• Pages: 742-748

Dates

published

1 - 8 - 2012

online

17 - 7 - 2012

Contributors

author

Juan Guirao

• Departamento de Matemática Aplicada y Estadística Universidad Politécnica de Cartagena, Hospital de Marina, 30203, Cartagena, Región de Murcia, Spain

author

Miguel López

• Departamento de Matemáticas, Universidad de Castilla-La Mancha, E.U. Politécnica de Cuenca, Campus Universitario, 16071, Cuenca, Castilla La-Mancha, Spain

author

Juan Vera

• Centro Universitario de la Defensa, Academia General del Aire, Universidad Politécnica de Cartagena, 30720, Santiago de la Ribera, Región de Murcia, Spain

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)

Identifiers

DOI

10.2478/s11534-012-0077-0