Dynamical properties of single-file diffusion

P. L. Krapivsky (1) , Kirone Mallick (2) , Tridib Sadhu (2)

1 BU - Boston University [Boston]
2 IPHT - Institut de Physique Théorique - UMR CNRS 3681

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.

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

Domaines: Physique [physics]

P. L. Krapivsky, Kirone Mallick, Tridib Sadhu. Dynamical properties of single-file diffusion. Journal of Statistical Mechanics: Theory and Experiment, 2015, 2015, pp.09007. ⟨10.1088/1742-5468/2015/09/P09007⟩. ⟨cea-01304779⟩