The Lasting Effect of Initial Conditions on Single File Diffusion

Abstract

We study the dynamics of a tagged particle in an environment of point Brownian particles with hard-core interactions in an infinite one dimensional channel (a single-file model). In particular we examine the influence of initial conditions on the dynamic of the tagged particle. We compare two initial conditions: equal distances between particles and uniform density distribution. The effect is shown by the differences of mean-square-displacement and correlation function for the two ensembles of initial conditions. We discuss the violation of Einstein relation, and its dependence on the initial condition, and the difference between time and ensemble averaging. More specifically, using the Jepsen line, we will discuss how transport coefficients, like diffusivity, depend on the initial state. Our work shows that initial conditions determine the long time limit of the dynamic, and in this sense the system never forgets its initial state in complete contrast with thermal systems (i.e a closed system which attains equilibrium independent of the initial state).

11 pages, 9 figures

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Cited by in corpus (57)

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• Single-file escape of colloidal particles from microfluidic channels
• Aging Wiener-Khinchin Theorem and Critical Exponents of $1/f$ Noise
• Large deviation function of a tracer position in single file diffusion
• Thermodynamic Uncertainty Relation Bounds the Extent of Anomalous Diffusion
• Scaling Green-Kubo relation and application to three aging systems
• Milestoning estimators of dissipation in systems observed at a coarse resolution: When ignorance is truly bliss
• Tracer dynamics in one dimensional gases of active or passive particles
• Role of initial conditions in $1D$ diffusive systems: compressibility, hyperuniformity and long-term memory
• Correlations of the density and of the current in non-equilibrium diffusive systems
• Scale invariant Green-Kubo relation for time averaged diffusivity
• Exact correlations in a single file system with a driven tracer
• Unfolding Tagged Particle Histories in Single-File Diffusion: Exact Single- and Two-Tag Local Times Beyond Large Deviation Theory
• Dynamical fluctuations in the Riesz gas
• Single-file transport in periodic potentials: The Brownian asymmetric exclusion process
• Effusion of stochastic processes on a line
• Diffusion of tagged particles in a crowded medium
• Ergodic property of Langevin systems with superstatistical, uncorrelated or correlated diffusivity
• Ergodic property of random diffusivity system with trapping events
• Single-file diffusion in a bi-stable potential: signatures of memory in the barrier-crossing of a tagged-particle
• Generalized disorder averages and current fluctuations in run and tumble particles
• Tagged particle in single-file diffusion with arbitrary initial conditions
• Single-file diffusion with non-thermal initial conditions
• Interacting single-file system: Fractional Langevin formulation versus diffusion-noise approach
• Insights from Single-File Diffusion into Cooperativity in Higher Dimensions
• $1/f^{\beta }$ noise for scale-invariant processes: How long you wait matters
• From Particle Currents to Tracer Diffusion: Universal Correlation Profiles in Single-File Dynamics
• Macroscopic fluctuations of a driven tracer in the symmetric exclusion process
• Driven transport of soft Brownian particles through pore-like structures: Effective size method
• Driven Tracer in the Symmetric Exclusion Process: Linear Response and Beyond
• Tracer dynamics in a single-file system with absorbing boundary
• Cumulant generating functions of a tracer in quenched dense symmetric exclusion processes
• Inhomogeneous diffusion and ergodicity breaking induced by global memory effects
• Single-File Diffusion of Active Brownian Particles
• Single-file diffusion in spatially inhomogeneous systems
• Novel anomalous diffusion phenomena of underdamped Langevin equation with random parameters
• Large deviations of a tracer position in the dense and the dilute limits of a single-file diffusion
• Stochastic thermodynamics of a tagged particle within a harmonic chain
• Scaling laws for single-file diffusion of adhesive particles
• BetheSF: Efficient computation of the exact tagged-particle propagator in single-file systems via the Bethe eigenspectrum
• First-passage dynamics of obstructed tracer particle diffusion in one-dimensional systems
• Uphill drift in the absence of current in single-file diffusion
• Tagged-Particle Statistics in Single-File Motion with Random-Acceleration and Langevin Dynamics
• Tracer dynamics in the active random average process
• Non-Fickian single-file pore transport
• Conserved densities of hard rods: microscopic to hydrodynamic solutions
• Emerging quasi-0D states at vanishing total entropy of the 1D hard sphere system: a coarse-grained similarity to the car parking problem
• Anomalously slow transport in single-file diffusion with slow binding kinetics
• Unexpected Effects of Disorder on Current Fluctuations in the Symmetric Simple Exclusion Process
• 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
• Current fluctuations in finite-sized one-dimensional non-interacting passive and active systems
• Single file diffusion meets Feynman path integral