破火山口势能面的相空间结构与输运
Phase Space Structure and Transport in a Caldera Potential Energy Surface
摘要：
我们研究相空间输运在一个二维破火山口势能面（PES）使用非线性动力学技术。破火山口PES的特点是一个平坦的区域或浅的最小值在其中心所包围的潜在的墙壁和多个对称性相关的指数一鞍点，允许入口和出口从这个中间regions.We已经发现了四个定性不同的情况下，相空间的结构，管理相空间运输。这些情况下进行分类，根据总能量和稳定性的周期轨道与家庭的中心最小值，同一家庭的分叉，和精力充沛的访问指数一鞍。在每种情况下，我们计算了不变流形的不稳定周期轨道的中心区域的潜在的和不变流形的不稳定周期轨道的家庭的周期轨道与指数为1的鞍。我们发现，有三个不同的机制所确定的不稳定周期轨道的不变流形结构支配相空间输运。第一种机制解释了从低能量鞍区进入破火山口的轨迹入口的性质，以及它们如何被困在潜在的中心区域。第二种机制描述了从破火山口中心区域开始的轨迹的捕获，它们到鞍状区域的运输，以及它们从破火山口出口的性质。第三种机制描述了相空间几何形状，负责最初由Carpenter提出的轨迹的动态匹配，并在Collins等人（2014）中描述了我们考虑的二维破火山口PES。
英文摘要：
We study phase space transport in a 2D caldera potential energy surface (PES) using techniques from nonlinear dynamics. The caldera PES is characterized by a flat region or shallow minimum at its center surrounded by potential walls and multiple symmetry related index one saddle points that allow entrance and exit from this intermediate region.We have discovered four qualitatively distinct cases of the structure of the phase space that govern phase space transport. These cases are categorized according to the total energy and the stability of the periodic orbits associated with the family of the central minimum, the bifurcations of the same family, and the energetic accessibility of the index one saddles. In each case we have computed the invariant manifolds of the unstable periodic orbits of the central region of the potential and the invariant manifolds of the unstable periodic orbits of the families of periodic orbits associated with the index one saddles. We have found that there are three distinct mechanisms determined by the invariant manifold structure of the unstable periodic orbits govern the phase space transport. The first mechanism explains the nature of the entrance of the trajectories from the region of the low energy saddles into the caldera and how they may become trapped in the central region of the potential. The second mechanism describes the trapping of the trajectories that begin from the central region of the caldera, their transport to the regions of the saddles, and the nature of their exit from the caldera. The third mechanism describes the phase space geometry responsible for the dynamical matching of trajectories originally proposed by Carpenter and described in Collins et al. (2014) for the two dimensional caldera PES that we consider.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
