Generalized Gaussian wave packet dynamics: Integrable and chaotic systems.
Generalized Gaussian wave packet dynamics: Integrable and chaotic systems.
复制标题
广义高斯波包动力学：可积系统和混沌系统。
DOI：
10.1103/physreve.93.012213
复制
发表时间：
2015
期刊：
影响因子：
--
通讯作者：
S. Tomsovic
中科院分区：
文献类型：
--
作者：
Harinder Pal;Manan Vyas;S. Tomsovic
最终的半经典波包传播技术是一种复杂的、时变的Wentzel-Kramers-Brillouin方法，即广义高斯波包动力学（GGWPD）。它需要克服许多技术上的困难，才能在实践中得到充分实施。在大约20年前，线性化波包动力学被推广到包括偏离中心的方法，经典可积和混沌动力系统的真实轨迹集，完全捕获动力输运。这些方法和GGWPD之间的连接是以一种更实际地实现GGWPD的方式开发的。在其基础上，一般复杂的鞍点轨迹是使用多维牛顿-拉夫森根搜索方法找到的，该方法从一组偏离中心的真实轨迹开始。这是可能的，因为存在一对一的对应关系。与每个偏离中心的真实轨迹相关联的邻近轨迹形成了一条穿过唯一鞍座的路径；有一些例外是很容易识别的。将该方法应用于被踢转子，以证明使用鞍点轨迹可以提高精度。
The ultimate semiclassical wave packet propagation technique is a complex, time-dependent Wentzel-Kramers-Brillouin method known as generalized Gaussian wave packet dynamics (GGWPD). It requires overcoming many technical difficulties in order to be carried out fully in practice. In its place roughly twenty years ago, linearized wave packet dynamics was generalized to methods that include sets of off-center, real trajectories for both classically integrable and chaotic dynamical systems that completely capture the dynamical transport. The connections between those methods and GGWPD are developed in a way that enables a far more practical implementation of GGWPD. The generally complex saddle-point trajectories at its foundation are found using a multidimensional Newton-Raphson root search method that begins with the set of off-center, real trajectories. This is possible because there is a one-to-one correspondence. The neighboring trajectories associated with each off-center, real trajectory form a path that crosses a unique saddle; there are exceptions that are straightforward to identify. The method is applied to the kicked rotor to demonstrate the accuracy improvement as a function of ℏ that comes with using the saddle-point trajectories.