Dynamical properties of single-file diffusion

Abstract

We study the statistics of a tagged particle in single-file diffusion, a one-dimensional interacting infinite-particle system in which the order of particles never changes. We compute the two-time correlation function for the displacement of the tagged particle for an arbitrary single-file system. We also discuss single-file analogs of the arcsine law and the law of the iterated logarithm characterizing the behavior of Brownian motion. Using a macroscopic fluctuation theory we devise a formalism giving the cumulant generating functional. In principle, this functional contains the full statistics of the tagged particle trajectory---the full single-time statistics, all multiple-time correlation functions, etc. are merely special cases.

20 pages, 1 figure

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Cited by in corpus (28)

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• Large deviations and dynamical phase transitions in stochastic chemical networks
• Extreme-Value Statistics of Fractional Brownian Motion Bridges
• Perturbative Expansion for the Maximum of Fractional Brownian Motion
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• Exact spatial correlations in single-file diffusion
• Generalised density profiles in single-file systems
• Anomalous scaling of dynamical large deviations of stationary Gaussian processes
• First passage in an interval for fractional Brownian motion
• Dynamical fluctuations in the Riesz gas
• Single-file transport in periodic potentials: The Brownian asymmetric exclusion process
• Duality relations in single-file diffusion
• Geometrical optics of large deviations of fractional Brownian motion
• Occupation time statistics of a gas of interacting diffusing particles
• Joint distribution of currents in the symmetric exclusion process
• From Particle Currents to Tracer Diffusion: Universal Correlation Profiles in Single-File Dynamics
• Cumulant generating functions of a tracer in quenched dense symmetric exclusion processes
• Solitons in fluctuating hydrodynamics of diffusive processes
• Large deviations of a tracer position in the dense and the dilute limits of a single-file diffusion
• 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
• Tracer dynamics in the active random average process
• Conserved densities of hard rods: microscopic to hydrodynamic solutions
• 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
• Single file diffusion meets Feynman path integral
• A Novel Mechanism of Ordering in a Coupled Driven System: Vacancy Induced Phase Separation