论文标题
复杂的相位空间，初始值表示和半经典繁殖的准确性
Complexified phase spaces, initial value representations, and the accuracy of semiclassical propagation
论文作者
论文摘要
使用相位空间络合率，在位置空间中的半经典传播器的初始值表示（IVR）作为反向Segal-Bargmann（S-B）变换的组成，对半经典相干态传播器的变换。结果表明，结果不含苛性奇异性，与Herman-Kluk（H-K）传播器相同，在物理和化学应用中发现了无处不在。我们将该特定IVR的理论方面与Van Vleck-Gutzwiller（VV-G）传播器及其IVR之一进行了对比，它通常用于逃避VV-G所需的轨迹的非线性“根系搜索”。我们证明，除了H-K繁殖器以外，绕过根搜索是以严重的数值不稳定的代价。我们使用均匀的Kerr系统进行的全面数值计算来备份理论论点，我们还揭示了一些意外的新现象，即：（1）观察半经典动力学中Ehrenfest时间的一半明确标记； （2）围绕苛性剂的轨迹的积累是时间增加的函数（称为“苛性粘性”）。我们期望这些现象比仅Kerr系统更一般。
Using phase-space complexification, an Initial Value Representation (IVR) for the semiclassical propagator in position space is obtained as a composition of inverse Segal-Bargmann (S-B) transforms of the semiclassical coherent state propagator. The result is shown to be free of caustic singularities and identical to the Herman-Kluk (H-K) propagator, found ubiquitously in physical and chemical applications. We contrast the theoretical aspects of this particular IVR with the van Vleck-Gutzwiller (vV-G) propagator and one of its IVRs, often employed in order to evade the non-linear "root-search" for trajectories required by vV-G. We demonstrate that bypassing the root-search comes at the price of serious numerical instability for all IVRs except the H-K propagator. We back up our theoretical arguments with comprehensive numerical calculations performed using the homogeneous Kerr system, about which we also unveil some unexpected new phenomena, namely: (1) the observation of a clear mark of half the Ehrenfest's time in semiclassical dynamics; and (2) the accumulation of trajectories around caustics as a function of increasing time (dubbed "caustic stickiness"). We expect these phenomena to be more general than for the Kerr system alone.
