表面跳跃传播子：扩散影响反应的另一种方法
Surface Hopping Propagator: An Alternative Approach to Diffusion-Influenced Reactions
摘要：
粒子在约束中扩散的动力学可以看作是约束表面上的一系列体扩散介导的跳跃。在这里，我们调查的表面跳跃传播，描述了扩散粒子的位置后，规定的数量的遇到该表面。这个量在受扩散影响的反应中起着核心作用，并决定了它们最常见的特性，如传播子、首次通过时间分布和反应速率。我们推导出明确的公式，表面跳跃传播和相关数量的几个欧几里德域：半空间，圆环，圆柱，球壳。这些结果为研究扩散介导的表面现象提供了理论基础。研究了“不朽”和“致命”粒子的表面跳跃传播子的行为。
英文摘要：
Dynamics of a particle diffusing in a confinement can be seen a sequence of bulk-diffusion-mediated hops on the confinement surface. Here, we investigate the surface hopping propagator that describes the position of the diffusing particle after a prescribed number of encounters with that surface. This quantity plays the central role in diffusion-influenced reactions and determines their most common characteristics such as the propagator, the first-passage time distribution, and the reaction rate. We derive explicit formulas for the surface hopping propagator and related quantities for several Euclidean domains: half-space, circular annuli, circular cylinders, and spherical shells. These results provide the theoretical ground for studying diffusion-mediated surface phenomena. The behavior of the surface hopping propagator is investigated for both "immortal" and "mortal" particles.
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