Generalised density profiles in single-file systems

Abstract

Single-file diffusion refers to the motion in narrow channels of particles which cannot bypass each other. These strong correlations between particles lead to tracer subdiffusion, which has been observed in contexts as varied as transport in porous media, zeolites or confined colloidal suspensions, and theoretically studied in numerous works. Most approaches to this celebrated many-body problem were restricted to the description of the tracer only, whose essential properties, such as large deviation functions or two-time correlation functions, were determined only recently. Here, we go beyond this standard description by introducing and determining analytically generalised density profiles (GDPs) in the frame of the tracer. In addition to controlling the statistical properties of the tracer, these quantities fully characterise the correlations between the tracer position and the bath particles density. Considering the hydrodynamic limit of the problem, we unveil universal scaling properties of the GDPs with space and time, and a non-monotonic dependence with the distance to the tracer despite the absence of any asymmetry. Our analytical approach provides exact results for the GDPs of paradigmatic models of single-file diffusion, such as Brownian particles with hardcore repulsion, the Symmetric Exclusion Process and the Random Average Process. The range of applicability of our approach is further illustrated by considering extensions to general interactions between particles and out-of-equilibrium situations.

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• Dynamical fluctuations in the Riesz gas
• Equation of state of hard-disk fluids under single-file confinement
• Duality relations in single-file diffusion
• Joint distribution of currents in the symmetric exclusion process
• From Particle Currents to Tracer Diffusion: Universal Correlation Profiles in Single-File Dynamics
• Driven Tracer in the Symmetric Exclusion Process: Linear Response and Beyond
• Tracer diffusion beyond Gaussian behavior: explicit results for general single-file systems
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• Monte Carlo simulation of Hard-, Square-Well, and Square-Shoulder Disks in narrow channels
• Semi-infinite simple exclusion process: from current fluctuations to target survival
• Tracer and current fluctuations in driven diffusive systems
• Exact time dependence of the cumulants of a tracer position in a dense lattice gas
• Current fluctuations in the symmetric exclusion process beyond the one-dimensional geometry
• Universal scale-free decay of tracer-bath correlations in $d$-dimensional interacting particle systems
• Tracer dynamics in the active random average process
• Unexpected Effects of Disorder on Current Fluctuations in the Symmetric Simple Exclusion Process
• Single file dynamics of tethered random walkers
• Exact large-scale correlations in diffusive systems with general interactions: explicit characterisation without the Dean--Kawasaki equation
• Exact fluctuation and long-range correlations in a single-file model under resetting
• Macroscopic fluctuation theory of interacting Brownian particles