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

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 Lévy flights. We further emphasise the generality of our results by showing that they also apply beyond the 1d case, and to other observables.

arXiv comment6 pages, 6 figures + 15 pages of supplementary material

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Cited by in corpus (6)

• Tagged particle behavior in a harmonic chain of direction reversing active Brownian particles
• Tracer and current fluctuations in driven diffusive systems
• Current fluctuations in the symmetric exclusion process beyond the one-dimensional geometry
• Systematic analysis of critical exponents in continuous dynamical phase transitions of weak noise theories
• Exact large-scale correlations in diffusive systems with general interactions: explicit characterisation without the Dean--Kawasaki equation
• Dynamics of soft interacting particles on a comb