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Set oriented computation of transport rates in 3-degree of freedom systems: the Rydberg atom in crossed fields

Dellnitz, M. and Grubits, K. A. and Marsden, J. E. and Padberg, K. and Thiere, B (2005) Set oriented computation of transport rates in 3-degree of freedom systems: the Rydberg atom in crossed fields. Regular and Chaotic Dynamics, 10 (2). pp. 173-192. ISSN 1560-3547.

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We present a new method based on set oriented computations for the calculation of reaction rates in chemical systems. The method is demonstrated with the Rydberg atom, an example for which traditional Transition State Theory fails. Coupled with dynamical systems theory, the set oriented approach provides a global description of the dynamics. The main idea of the method is as follows. We construct a box covering of a Poincaré section under consideration, use the Poincaré first return time for the identification of those regions relevant for transport and then we apply an adaptation of recently developed techniques for the computation of transport rates ([12], [27]). The reaction rates in chemical systems are of great interest in chemistry, especially for realistic three and higher dimensional systems. Our approach is applied to the Rydberg atom in crossed electric and magnetic fields. Our methods are complementary to, but in common problems considered, agree with, the results of [14]. For the Rydberg atom, we consider the half and full scattering problems in both the 2- and the 3-degree of freedom systems. The ionization of such atoms is a system on which many experiments have been done and it serves to illustrate the elegance of our method.

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Additional Information:© 2005, Received May 17, 2005; accepted May 30, 2005. The authors thank Frederic Gabern, Oliver Junge, Wang S. Koon and Shane D. Ross for helpful discussions and comments. This work was partly supported by the German Science Foundation (DFG) Project SFB-376, the DFG Priority Program 1095, a Max Planck Research Award, and ARO grant DAAD19-03-D-0004 through the Santa Barbara ICB.
Funding AgencyGrant Number
German Science Foundation (DFG)SFB-376
German Science Foundation (DFG) 1095
Max Planck Research UNSPECIFIED
Army Research Office (ARO)DAAD19-03-D-0004
Subject Keywords:dynamical systems, transport rates, set oriented methods, invariant manifolds, Poincare map, return times, ionization, atoms in crossed Fields
Classification Code:MSC: 37N20, 37M05, 37M25, 37J15, 92E20
Record Number:CaltechAUTHORS:20100802-071646308
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Official Citation:M Dellnitz, K A Grubits, J E Marsden, K Padberg, B Thiere, "Set oriented computation of transport rates in 3-degree of freedom systems: the Rydberg atom in crossed fields", REGUL CHAOTIC DYN, 2005, 10 (2), 173–192
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:19236
Deposited By: Ruth Sustaita
Deposited On:02 Aug 2010 21:48
Last Modified:26 Dec 2012 12:16

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