On the Regularity and Chaos of the Hydrogen Atom Subjected to External Fields

作     者：Jaouad Kharbach Walid Chatar Mohamed Benkhali Abdellah Rezzouk Mohammed Ouazzani-Jamil 

作者机构：Laboratoire de Physique du Solide Faculté des Sciences Dhar El Mahraz Université Sidi Mohamed Ben Abdellah Fès-Atlas Morocco Université Privée de Fès Laboratoire Systèmes et Environnements Durables Lot. Quaraouiyine Route Ain Chkef Fès Mo-rocco 

出 版 物：《International Journal of Modern Nonlinear Theory and Application》 (现代非线性理论与应用（英文）)

年 卷 期：2018年第7卷第2期

页      面：56-76页

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

主　　题：Hydrogen Atom Zeeman Effect Stark Effect Van Der Waals Interaction Hamiltonian System Integrability Bifurcation Chaos Poincaré Surfaces of Section 

摘      要：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.