Berezhkovskii A M
Mathematical and Statistical Computing Laboratory, Division of Computational Bioscience, Center for Information Technology, National Institutes of Health, Bethesda, MD 20892, USA.
Chem Phys. 2010 May 1;370(1-3):253-257. doi: 10.1016/j.chemphys.2009.10.020.
Path integral based approach is used to analyze the variance of the residence time spent in a sub-domain by a particle diffusing in the presence of an arbitrary potential in a larger domain containing the sub-domain. It is assumed that there is no absorption of the particle within the domain or at its boundaries. Because of the ergodisity, the mean residence time in the sub-domain is a product of the observation time and the equilibrium probability of finding the particle in the sub-domain. We show that the variance also grows linearly with the observation time at large times and explain how the slope of this linear dependence can be found. The general approach is illustrated by simple examples, in which explicit formulas for the variance can be obtained.
基于路径积分的方法用于分析在包含子域的更大区域中，粒子在任意势场存在下扩散时在子域中停留时间的方差。假设在该区域内及其边界处不存在粒子吸收。由于遍历性，子域中的平均停留时间是观测时间与在子域中找到粒子的平衡概率的乘积。我们表明，在较长时间内方差也随观测时间线性增长，并解释了如何找到这种线性依赖关系的斜率。通过简单示例说明了一般方法，在这些示例中可以获得方差的显式公式。
