外场作用下的一维无规行走过程及其性质

本文较系统地对外场作用下的一维无规行走过程及其若干性质进行了研究。在分立与连续随机变量两种情况下,首先建立了概率演化的Markov链方程,然后在最近邻偏向行走的模型下,求出了它们的严格的解析解,最后利用这些解析解讨论了这个过程的由一些结果所表征的输运性质与统计性质。

ONE-DIMENTIONAL RANDOM WALK PROCESS AND ITS PROPERTIES UNDER AN APPLIED FIELD

In this paper,one-dimensional random walk process and its many propertiesunder the action of an applied field are investigated systematically and in detail.FirstMarkov chain type of equations for the probability evolution are established withstochastic variables being discrete and continuous,then their exact analytic soluti-ons are obtained for the biased walk model with the nearest-neighbor steps,andfinally many interesting transport and statistical properties of this process are disc-ussed which are characterized by the many results.A characteristic common tothese results but different from that of the symmetric(unbiased)walk without theaction of no applied field lies in the direct and explicit dependence of them onthe applied field hence on time,i.e.,is dispersive.In particular,the dispersiveeffect disappears with the field when it is switched off and then many correspo-nding results to the unbiased(sysmmetric)walk are obtained immediately,whichmakes the present discussion more general.