Charles University in Prague, Faculty of Mathematics and Physics, Department of Macromolecular Physics, V Holešovičkách 2, 180 00 Praha, Czech Republic.
J Chem Phys. 2013 Apr 21;138(15):154104. doi: 10.1063/1.4801326.
We investigate the long-time behavior of the survival probability of a tagged particle in a single-file diffusion in a finite interval. The boundary conditions are of two types: (1) one boundary is absorbing the second is reflecting and (2) both boundaries are absorbing. For each type of the boundary conditions we consider two types of initial conditions: (a) initial number of particles N is given and (b) initial concentration of particles is given (N is random). In all four cases the tagged-particle survival probability exhibits different asymptotic behavior. When the both boundaries are absorbing we also consider a case of a random interval length (single-file diffusion on a line with randomly distributed traps). In the latter setting, the initial concentration of particles has the same effect on the asymptotic decay of the survival probability as the concentration of traps.
我们研究了在有限区间中单分子扩散中标记粒子的存活概率的长时间行为。边界条件有两种类型：（1）一个边界是吸收的，另一个边界是反射的；（2）两个边界都是吸收的。对于每种边界条件，我们考虑两种初始条件：（a）给定初始粒子数 N；（b）给定初始粒子浓度（N 是随机的）。在所有四种情况下，标记粒子的存活概率表现出不同的渐近行为。当两个边界都是吸收的时，我们还考虑了随机间隔长度的情况（在线上具有随机分布的陷阱的单分子扩散）。在后一种情况下，初始粒子浓度对存活概率的渐近衰减具有与陷阱浓度相同的影响。
