From Particle Currents to Tracer Diffusion: Universal Correlation Profiles in Single-File Dynamics

TL;DR

This paper demonstrates that correlation profiles in single-file particle systems have a universal form at any time, regardless of the specific stochastic dynamics, with applications to various models and observables.

Contribution

It introduces a universal form for correlation profiles in single-file systems with arbitrary stochastic dynamics, extending beyond diffusive models and one-dimensional cases.

Findings

Correlation profiles are universal at all times.

Results apply to Brownian, run-and-tumble, and Lévy flight models.

The approach extends beyond 1D and to different observables.

Abstract

Single-file transport refers to the motion of particles in a narrow channel, such that they cannot bypass each other. This constraint leads to strong correlations between the particles, described by correlation profiles, which measure the correlation between a generic observable and the density of particles at a given position and time. They have recently been shown to play a central role in single-file systems. Up to now, these correlations have only been determined for diffusive systems in the hydrodynamic limit. Here, we consider a model of reflecting point particles on the infinite line, with a general individual stochastic dynamics. We show that the correlation profiles take a simple universal form, at arbitrary time. We illustrate our approach by the study of the integrated current of particles through the origin, and apply our results to representative models such as Brownian particles, run-and-tumble particles and L\'evy flights. We further emphasise the generality of our results by showing that they also apply beyond the 1d case, and to other observables.