相空间反应散射的量子理论
Quantum Theory of Reactive Scattering in Phase Space
摘要：
我们回顾了最近的结果量子反应散射从相空间的角度来看。该方法使用经典和量子版本的规范形式理论和动力系统理论的观点。在过去的十年中，经典的规范形理论提供了一种方法来实现相空间结构，负责确定反应的高维哈密顿系统。这导致了一种新的（反应动力学）类型的相空间结构的理解，一个{ \em正常双曲不变流形}（或，NHIM）是“锚”上的相空间结构控制反应动力学的建立。量子标准形理论提供了一种通过使用外尔量子化过程来量子化这些相空间结构的方法。我们表明，这种方法提供了一个解决方案的时间无关的薛定谔方程导致（本地）的S-矩阵的鞍点附近的反应。很容易得出，通过具有上述性质的分割表面的定向通量的量化是可以以“封闭形式”表示的通量算子。此外，从局部S-矩阵，我们很容易得到的累积反应概率（CRP）的表达式。值得注意的是，CRP的表达式可以在不需要计算经典轨迹的情况下进行评估。NHIM的量子化导致激活的复合物，并且在NHIM上初始化的量子态的寿命对应于Gamov-Siegert共振。我们将这些结果应用到共线氮交换反应和一个三自由度系统对应的Eckart屏障耦合到两个Morse振荡器。
英文摘要：
We review recent results on quantum reactive scattering from a phase space perspective. The approach uses classical and quantum versions of normal form theory and the perspective of dynamical systems theory. Over the past ten years the classical normal form theory has provided a method for realizing the phase space structures that are responsible for determining reactions in high dimensional Hamiltonian systems. This has led to the understanding that a new (to reaction dynamics) type of phase space structure, a {\em normally hyperbolic invariant manifold} (or, NHIM) is the "anchor" on which the phase space structures governing reaction dynamics are built. The quantum normal form theory provides a method for quantizing these phase space structures through the use of the Weyl quantization procedure. We show that this approach provides a solution of the time-independent Schrödinger equation leading to a (local) S-matrix in a neighborhood of the saddle point governing the reaction. It follows easily that the quantization of the directional flux through the dividing surface with the properties noted above is a flux operator that can be expressed in a "closed form". Moreover, from the local S-matrix we easily obtain an expression for the cumulative reactio probability (CRP). Significantly, the expression for the CRP can be evaluated without the need to compute classical trajectories. The quantization of the NHIM is shown to lead to the activated complex, and the lifetimes of quantum states initialized on the NHIM correspond to the Gamov-Siegert resonances. We apply these results to the collinear nitrogen exchange reaction and a three degree-of-freedom system corresponding to an Eckart barrier coupled to two Morse oscillators.
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