论氢原子在外场作用下的规律性和混沌性

J. Kharbach, W. Chatar, M. Benkhali, A. Rezzouk, M. Ouazzani-Jamil
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引用次数: 3

摘要

本文研究了氢原子在三个静态外场作用下的可积经典情况。探讨了实相空间的结构和演化。给出了分岔图,并讨论了解的分岔问题。明确地描述了运动第一积分的奇异公共水平集的周期解及其相关周期。利用截面Poincare曲面对可积情况进行了数值研究,并将其与附近的活的不可积分解进行了比较,说明了所有改变相空间结构的一般分岔;该问题在一定的系统控制参数范围内可以表现出规律的混沌过渡。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
On the Regularity and Chaos of the Hydrogen Atom Subjected to External Fields
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 Poincare 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.
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