Phase space structure of the hydrogen atom in a circularly polarized microwave field

Abstract

We consider the problem of the hydrogen atom interacting with a circularly polarized microwave field, modeled as a perturbed Kepler problem. A remarkable feature of this system is that the electron can follow what we term erratic orbits before ionizing. In an erratic orbit the electron makes multiple large distance excursions from the nucleus with each excursion being followed by a close approach to the nucleus, where the interaction is large. Here we are interested in the mechanisms that explain this observation. We find that the manifolds associated with certain hyperbolic periodic orbits may play an important role, despite the fact that, in some respects, the dynamics is almost Keplerian. A study of some relevant invariant objects is carried out for different system parameters. The consequences of our findings for ionization of an electron by the external field are also discussed.

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

“…Barrabés et al study [1] the dynamics of the hydrogen atom under the effects of a circularly polarized microwave field, through the use of a model coming from the celestial mechanics, as a planar perturbed Kepler problem for some particular cases of the parameter.…”

“…In the long and well written introduction of [1] the importance of this mechanic system is stated, so we do not go further into this point and we refer the reader to that paper and the references therein. Nevertheless, for this model, we underline the dynamical consequences of a possible non-integrability like chaotic movements for some trajectories of the system and certain dynamical complexity given by the exhibition of a variety of phenomena that remain poorly understood.…”

“…Thus, our objective in this paper is to prove in an analytical way the 1 non-integrability of this problem for any value of the parameter. In [1] only some numerical evidence of this fact were presented for some particular values of the parameter.…”

“…In [1] only some numerical evidence of this fact were presented for some particular values of the parameter. This result open the door for other studies focused on trying to understand the chaotic behavior of this system.…”

“…The analysis of the smooth integrability of a Hamiltonian system is an important problem from the dynamical point of view to understand the behavior of a system. After consulting the authors of [1], and as far as we know, an analytical proof of the 1 non-integrability of this problem has not been given yet. We present an analytical proof using methods coming from the averaging theory for studying periodic orbits of dynamical systems, see [6].…”