Dynamical properties of single-file diffusion

作者：Krapivsky P L^*; Mallick Kirone; Sadhu Tridib

来源：Journal of Statistical Mechanics: Theory and Experiment , 2015, 2015(9): P09007.

DOI：10.1088/1742-5468/2015/09/P09007

• stochastic particle dynamics (theory)
• stochastic processes (theory)
• brownian motion

We study the statistics of a tagged particle in single-file diffusion, a one-dimensional interacting infinite-particle system in which the order of particles never changes. We compute the two-time correlation function for the displacement of the tagged particle for an arbitrary single-file system. We also discuss single-file analogs of the arcsine law and the law of the iterated logarithm characterizing the behavior of Brownian motion. Using a macroscopic fluctuation theory we devise a formalism giving the cumulant generating functional. In principle, this functional contains the full statistics of the tagged particle trajectory-the full single-time statistics, all multiple-time correlation functions, etc are merely special cases.

• 出版日期2015-9
• 单位中国地震局