论文标题
限制两个扩散粒子的第一次爆发时间
First-encounter time of two diffusing particles in confinement
论文作者
论文摘要
我们研究了限制如何在两个散射粒子的情况下如何彻底改变第一次接触时间的概率密度和相关的生存概率。为了获得对此问题的分析见解，我们专注于两个一维设置：半线和一个间隔。我们首先考虑具有相等的粒子扩散率的情况，为此，可以在全日制域上获得生存概率和相关的第一次接触时间密度的确切结果。我们还评估了它们存在的第一阶段时刻。然后，我们转向扩散性不相等的情况，并关注生存概率的长期行为。我们的结果突出了边界效应在扩散控制动力学中的重大影响，即使对于简单的一维设置，以及在这种系统的翻译不变性后，很难获得分析结果。
We investigate how confinement may drastically change both the probability density of the first-encounter time and the related survival probability in the case of two diffusing particles. To obtain analytical insights into this problem, we focus on two one-dimensional settings: a half-line and an interval. We first consider the case with equal particle diffusivities, for which exact results can be obtained for the survival probability and the associated first-encounter time density over the full time domain. We also evaluate the moments of the first-encounter time when they exist. We then turn to the case when the diffusivities are not equal, and focus on the long-time behavior of the survival probability. Our results highlight the great impact of boundary effects in diffusion-controlled kinetics even for simple one-dimensional settings, as well as the difficulty of obtaining analytic results as soon as translational invariance of such systems is broken.
