We analyze benchmark models for reaction dynamics associated with a time-dependent saddle point. Our model allows us to incorporate time dependence of a general form, subject to an exponential growth restriction. Under these conditions, we analytically compute the time-dependent normally hyperbolic invariant manifold; its time-dependent stable and unstable manifolds; and a time-dependent dividing surface that has the no-recrossing property. Consideration of the time dependence of these phase space structures is necessary in order to precisely capture reacting and nonreacting trajectories. Moreover, we show that a time-dependent dividing surface is necessary in order to eliminate recrossing in the time-dependent setting. In other words, if the dividing surface is not time-dependent, recrossing may occur.

中文翻译：

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时变相空间结构在反应动力学中的作用和分割表面的不交叉特性

我们分析了与时间相关的鞍点相关的反应动力学基准模型。我们的模型允许我们结合一般形式的时间依赖性，受指数增长限制。在这些条件下，我们分析计算了时间相关的正常双曲不变流形；其随时间变化的稳定和不稳定流形；以及具有不可重交特性的时间相关分割面。为了精确地捕捉反应和非反应轨迹，必须考虑这些相空间结构的时间依赖性。此外，我们表明，时间相关的划分面是必要的，以消除时间相关设置中的重新交叉。换言之，如果分割面不依赖于时间，则可能会发生重新交叉。