Exact correlations in a single file system with a driven tracer

TL;DR

This paper analyzes the correlations and fluctuations of particles in a single-file system with a driven tracer, deriving exact scaling functions for different initial conditions and revealing subdiffusive and superdiffusive behaviors.

Contribution

It provides exact calculations of two-point correlations and fluctuations in a driven tracer system under various initial conditions, extending understanding of single-file dynamics.

Findings

Correlations grow as Tb7 in steady states.

Exact scaling functions are derived for specific initial conditions.

Fluctuations grow superdiffusively as T^{3/2} for linearly increasing gaps.

Abstract

We study the effect of a single driven tracer particle in a bath of other particles performing the random average process on an infinite line using a stochastic hydrodynamics approach. We consider arbitrary fixed as well as random initial conditions and compute the two-point correlations. For quenched uniform and annealed steady state initial conditions we show that in the large time $T$ limit the fluctuations and the correlations of the positions of the particles grow subdiffusively as $\sqrt{T}$ and have well defined scaling forms under proper rescaling of the labels. We compute the corresponding scaling functions exactly for these specific initial configurations and verify them numerically. We also consider a non translationally invariant initial condition with linearly increasing gaps where we show that the fluctuations and correlations grow superdiffusively as $T^{3/2}$ at large times.