On the Regularity and Chaos of the Hydrogen Atom Subjected to External Fields
Open Access
- 1 January 2018
- journal article
- research article
- Published by Scientific Research Publishing, Inc. in International Journal of Modern Nonlinear Theory and Application
- Vol. 07 (02), 56-76
- https://doi.org/10.4236/ijmnta.2018.72005
Abstract
In this paper, the integrable classical case of the Hydrogen atom subjected to three static external fields is investigated. The structuring and evolution of the real phase space are explored. The bifurcation diagram is found and the bifurcations of solutions are discussed. The periodic solutions and their associated periods for singular common-level sets of the first integrals of motion are explicitly described. Numerical investigations are performed for the integrable case by means of Poincaré surfaces of section and comparing them with nearby living nonintegrable solutions, all generic bifurcations that change the structure of the phase space are illustrated; the problem can exhibit regularity-chaos transition over a range of control parameters of system.Keywords
This publication has 21 references indexed in Scilit:
- Rydberg states of the hydrogen atom in the instantaneous van der Waals potential: quantum mechanical, classical and semiclassical treatmentJournal of Physics B: Atomic, Molecular and Optical Physics, 2000
- Experimental Study of Quantum Dynamics in a Regime of Classical Anomalous DiffusionPhysical Review Letters, 1998
- Classical and quantum mechanics of an integrable limit of the hydrogen atom in combined circularly polarized microwave and magnetic fieldsPhysical Review A, 1998
- Quantum Chaos, Irreversible Classical Dynamics, and Random Matrix TheoryPhysical Review Letters, 1996
- The importance of resonances in microwave “ionization” of excited hydrogen atomsPhysics Reports, 1995
- Quantum chaos of the hydrogen atom in a generalized van der Waals potentialPhysical Review A, 1993
- Painlevé analysis, Lie symmetries, and integrability of coupled nonlinear oscillators of polynomial typePhysics Reports, 1993
- Dynamics of atomic hydrogen in a generalized van der Waals potentialPhysical Review A, 1990
- Electromagnetic traps for charged and neutral particlesReviews of Modern Physics, 1990
- Dynamical symmetries of the perturbed hydrogen atom: The van der Waals interactionPhysical Review Letters, 1987