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.
| Original language | English |
|---|---|
| Article number | P09007 |
| Journal | Journal of Statistical Mechanics: Theory and Experiment |
| Volume | 2015 |
| Issue number | 9 |
| DOIs | |
| Publication status | Published - 1 Sept 2015 |
| Externally published | Yes |
Keywords
- brownian motion
- stochastic particle dynamics (theory)
- stochastic processes (theory)