Dynamical properties of single-file diffusion. (8th September 2015)

• Record Type: Journal Article
• Authors: Krapivsky, P L; Mallick, Kirone; Sadhu, Tridib
• Is Part Of: Journal of statistical mechanics. (2015:Sep.)
• Publication Date: 2015-09-08
• Subjects: 4 -- 9 -- 15; 4/220 -- 9/300 -- 15/010; Statistical mechanics -- Periodicals; Mechanics -- Statistical methods -- Periodicals; 530.1305
• DOI: 10.1088/1742-5468/2015/09/P09007
• Languages: English
• ISSNs: 1742-5468

Abstract

Abstract: 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.