由稳定流型和不稳定流型证实氢原子的粘性效应

本文研究了氢原子哈密顿系统暴露在强激光场下的粘性效应,即使对于单电子系统,其庞加莱截面也显示出了由激光场引起的混沌部分和规则部分,并可以用KAM理论来解释.通过变分方法对混沌“海”中的不稳定周期轨道进行了寻找,并数值求解了相应的稳定流形和不稳定流形.研究结果表明,单电子系统电离的动力学性质由不稳定周期轨迹控制.一方面,不稳定周期轨迹的稳定流形很好地与递归图叠加在一起,表明稳定流形只与相空间中稳定的初始点重叠.另一方面,不稳定流形几乎与庞加莱表面上密集分布的点重合.这表明不稳定流形只是通过激光场驱动轨迹演化的电离通道.此外,在稳定流形与不稳定流形相互穿插的不稳定岛附近的不同区域的存活概率也被深入研究.它们服从代数衰减规律.相同的衰减趋势也出现在不稳定流形上,它们具有与不稳定周期轨迹附近区域相近的衰减参数.这些观察证实了不稳定周期轨迹的稳定性对在KAM稳定岛附近相空间的粘滞效应起着非常重要的作用.

The stickiness effect of Hydrogen atom evidenced by stable and unstable manifolds

In this paper, we investigated the stickiness effect of the Hamilton system of the Hydrogen atom exposed to intense laser field. Even for the one electron system, its Poincare surface of section shows the chaotic and regular parts due to the laser field which can be explained by KAM (Kolmogorov, Arnold, and Moser) theory. The unstable periodic orbit (UPO) in chaotic "sea" was located by variational method and the corresponding stable manifold (SM) and unstable manifold (UM) of the UPO were numerically calculated. It was shown that the dynamics of ionization of the one electron system is governed by the UPO. On one hand, the SM of UPO is well superposed with the recurrence plot, which indicates that the SM overlaps just the stable initial points in phase space. On the other hand, the UM is almost coincide with the densely distributed points on Poincare surface of section. This indicated that the UM is just the ionization channels of the trajectories driven by laser field. Furthermore, the survival probabilities of different regions which gradually cross the UM and SM tangential flow nearby the stable island are studied. They obey an algebraic decaying law. The similar decay trend are also observed on different regions on the UM which possess almost the same decay parameters with that of region nearby the UPO. These observations confirmed that the stability properties of UPO play very important role in the stickiness effect of the phase space nearby the KAM stable islands.