论文标题
在一个和二维晶格上进行主动随机步行的第一段统计数据
First passage statistics of active random walks on one and two dimensional lattices
论文作者
论文摘要
我们研究了一个主动连续时间随机步行的第一个段落统计数据，其中泊松等待时间分布在一维无限晶格和二维无限方晶格上。我们研究了首次返回到原点的概率的较小和较大的时间特性，以及第一次通过任意晶格位点的概率。众所周知，活性粒子的职业概率类似于普通的布朗运动的占用概率，该运动在大时具有有效的扩散常数。有趣的是，我们证明，即使在领先顺序，第一个段落概率也不是由简单的有效扩散常数给出的。我们证明，在后期，活动提高了第一次返回到原点的概率，以及第一次通过到足够接近原点的晶格位点的概率，我们根据péclet数量进行了量化。此外，我们得出了对称随机步行者的第一个段落概率和一个无偏见的随机助行器，而无需活动作为限制情况。我们通过在一个和二维中对主动随机步行者进行动力学蒙特卡洛模拟来验证我们的分析结果。
We investigate the first passage statistics of active continuous time random walks with Poissonian waiting time distribution on a one dimensional infinite lattice and a two dimensional infinite square lattice. We study the small and large time properties of the probability of the first return to the origin as well as the probability of the first passage to an arbitrary lattice site. It is well known that the occupation probabilities of an active particle resemble that of an ordinary Brownian motion with an effective diffusion constant at large times. Interestingly, we demonstrate that even at the leading order, the first passage probabilities are not given by a simple effective diffusion constant. We demonstrate that at late times, activity enhances the probability of the first return to the origin and the probabilities of the first passage to lattice sites close enough to the origin, which we quantify in terms of the Péclet number. Additionally, we derive the first passage probabilities of a symmetric random walker and a biased random walker without activity as limiting cases. We verify our analytic results by performing kinetic Monte Carlo simulations of an active random walker in one and two dimensions.
