Skip to content
BY-NC-ND 3.0 license Open Access Published by De Gruyter Open Access July 17, 2012

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

Juan Guirao, Miguel López and Juan Vera
From the journal Open Physics

Abstract

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.

[1] E. Barrabés, M. Ollé, F. Borondo, D. Farrelly, J. Mondelo, Physica D 241, 333 (2012) http://dx.doi.org/10.1016/j.physd.2011.10.01610.1016/j.physd.2011.10.016Search in Google Scholar

[2] R. Abraham, J. E. Marsden, Foundations of Mechanics, (Benjamin, Reading, Masachusets, 1978) Search in Google Scholar

[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) 10.1007/978-3-540-48926-9Search in Google Scholar

[4] A. Deprit, Celest. Mech. Dyn. Ast. 51, 201 (1991) http://dx.doi.org/10.1007/BF0005169110.1007/BF00051691Search in Google Scholar

[5] H. Poincaré, Les méthodes nouvelles de la mécanique céleste, Vol. I, (Gauthier-Villars, Paris 1899) 10.1007/BF02742713Search in Google Scholar

[6] F. Verhulst, Nonlinear Differential Equations and Dynamical Systems, (Universitext, Springer, 1991) 10.1007/978-3-642-97149-5Search in Google Scholar

[7] E. T. Whittaker, A Treatise on the Analytical Dynamics of Particles and Rigid Bodies, Cambridge Mathematical Library, (Cambridge University Press, 1989) Search in Google Scholar

Published Online: 2012-7-17
Published in Print: 2012-8-1

© 2012 Versita Warsaw

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Scroll Up Arrow