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* Corresponding author 1 BU - Boston University Boston 2 IPHT - Institut de Physique Théorique - UMR CNRS 3681

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.

Keywords : Tagged particle Single-file diffusion Macroscopic fluctuation theory Law of the iterated logarithm Arcsine law

Author: P. L. Krapivsky - Kirone Mallick - Tridib Sadhu -

Source: https://hal.archives-ouvertes.fr/


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