窄逃逸时间问题：不完美捕获情形
Narrow-escape-time problem: the imperfect trapping case
摘要：
我们提出了一个主方程方法的\emph{narrow escape time}（NET）的问题，即所需的时间为一个封闭的域与一个单一的狭窄的开口，退出域的第一次。我们引入了一个有限的跃迁概率，$ν$，在狭窄的逃逸窗口，允许研究的不完善的捕获情况。范围从0到$\infty$，$ν$允许研究捕获过程的两个极端：高度不足的捕获和逃逸是肯定的情况（“完美捕获”情况）。我们已经得到了分析结果的基本量研究的NET问题，\emph{mean escape time}（MET），我们已经研究了它的依赖性方面的过渡（解吸）概率（从）的表面边界，限制域尺寸，并在逃逸窗口的有限过渡概率。特别是，我们表明，存在一个全球性的最低限度，在NET依赖于“不完美”的诱捕过程。除了我们的分析方法，我们已经实施了蒙特卡罗模拟，发现理论结果和模拟之间的良好协议。
英文摘要：
We present a master equation approach to the \emph{narrow escape time} (NET) problem, i.e. the time needed for a particle contained in a confining domain with a single narrow opening, to exit the domain for the first time. We introduce a finite transition probability, $ν$, at the narrow escape window allowing the study of the imperfect trapping case. Ranging from 0 to $\infty$, $ν$ allowed the study of both extremes of the trapping process: that of a highly deficient capture, and situations where escape is certain ("perfect trapping" case). We have obtained analytic results for the basic quantity studied in the NET problem, the \emph{mean escape time} (MET), and we have studied its dependence in terms of the transition (desorption) probability over (from) the surface boundary, the confining domain dimensions, and the finite transition probability at the escape window. Particularly we show that the existence of a global minimum in the NET depends on the `imperfection' of the trapping process. In addition to our analytical approach, we have implemented Monte Carlo simulations, finding excellent agreement between the theoretical results and simulations.
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