Iñarrea M, Salas J P, Lanchares V
Area de Física Aplicada, Universidad de La Rioja, Edificio Científico Tecnológico, C/Madre de Dios 51, 26006 Logroño, Spain.
Phys Rev E Stat Nonlin Soft Matter Phys. 2002 Nov;66(5 Pt 2):056614. doi: 10.1103/PhysRevE.66.056614. Epub 2002 Nov 26.
We investigate the classical dynamics of a hydrogen atom in the presence of uniform magnetic and quadrupolar electric fields. After some reductions, the system is described by a two degree of freedom Hamiltonian depending on two parameters. On the one hand, it depends on the z component of the canonical angular momentum P(phi), which is an integral because the system is axially symmetric; and on the other it also depends on a parameter representing the relative field strengths. We note that this Hamiltonian is closely related to the one describing the generalized van der Waals interaction. We report three cases of integrability. The structure and evolution of the phase space are explored intensively by means of Poincaré surfaces of section when the parameters vary. In this sense, we find several bifurcations that strongly change the phase space structure. The chaotic behavior of the system is studied and three order-chaos transitions are found when the system passes through the integrable cases. Finally, the ionization mechanics is studied.
我们研究了在均匀磁场和四极电场存在下氢原子的经典动力学。经过一些简化后，该系统由一个依赖于两个参数的二维自由度哈密顿量来描述。一方面，它依赖于正则角动量(P(\phi))的(z)分量，由于系统具有轴对称性，所以这是一个积分量；另一方面，它还依赖于一个表示相对场强的参数。我们注意到这个哈密顿量与描述广义范德瓦尔斯相互作用的哈密顿量密切相关。我们报告了三种可积性情况。当参数变化时，通过庞加莱截面深入探索了相空间的结构和演化。从这个意义上说，我们发现了几个强烈改变相空间结构的分岔点。研究了系统的混沌行为，并发现当系统经过可积情况时会发生三次有序 - 混沌转变。最后，研究了电离机制。
