ANALYTIC CONTINUATION OF CLASSICAL MECHANICS FOR CLASSICALLY FORBIDDEN COLLISION PROCESSES.
ANALYTIC CONTINUATION OF CLASSICAL MECHANICS FOR CLASSICALLY FORBIDDEN COLLISION PROCESSES.
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经典禁止碰撞过程的经典力学的解析延续。
DOI：
10.1063/1.1677086
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发表时间：
1972
影响因子：
4.4
通讯作者：
T. George
中科院分区：
文献类型：
--
作者：
W. Miller;T. George
经典禁止过程是指那些不能通过普通经典动力学发生的过程。然而，在经典S -矩阵理论的框架内，经典力学可以解析地继续，并且对于这些经典禁止的或弱过渡振幅（即S -矩阵元素）可以获得经典极限近似。对复杂动力系统进行经典力学解析连续的最有效和最普遍的方法是通过相空间中经典无法到达的区域对运动方程本身进行积分。在这项工作中，成功地计算了这些分析连续轨迹；通过识别和考虑这些复值轨迹的某些特殊特征，可以看出它们本质上与普通（即真实）经典轨迹一样容易处理。应用于A+BC线性碰撞（振动激发）得到了很好的结果；跃迁概率小到10−11(小…
Classically forbidden processes are those that cannot take place via ordinary classical dynamics. Within the framework of classical S‐matrix theory, however, classical mechanics can be analytically continued and classical‐limit approximations obtained for these classically forbidden, or weak transition amplitudes (i.e., S‐matrix elements). The most powerful and general way of analytically continuing classical mechanics for a complex dynamical system is to integrate the equations of motion themselves through the classically inaccessible regions of phase space. Success in calculating these analytically continued trajectories is reported in this work; with certain special features of these complex‐valued trajectories recognized and taken account of, it is seen that they are essentially as easy to deal with numerically as ordinary (i.e., real) classical trajectories. Application to the linear A+BC collision (vibrational excitation) gives excellent results; transition probabilities as small as 10−11 (the small...