Universal Large Deviations for the Tagged Particle in Single File Motion

TL;DR

This paper derives an exact, universal large deviation function for the displacement of a tagged particle in a one-dimensional single-file system, regardless of whether particle dynamics are diffusive or ballistic.

Contribution

It provides the first exact calculation of the large deviation function for tagged particle motion, demonstrating its universality across different dynamical regimes.

Findings

Large deviation function is universal for diffusive and ballistic dynamics.

Exact analytical expression for the large deviation function is obtained.

Tagged particle motion exhibits sub-diffusive or diffusive behavior depending on dynamics.

Abstract

We consider a gas of point particles moving in a one-dimensional channel with a hard-core inter-particle interaction that prevents particle crossings --- this is called single-file motion. Starting from equilibrium initial conditions we observe the motion of a tagged particle. It is well known that if the individual particle dynamics is diffusive, then the tagged particle motion is sub-diffusive, while for ballistic particle dynamics, the tagged particle motion is diffusive. Here we compute exactly the large deviation function for the tagged particle displacement and show that this is universal, independent of the individual dynamics.