Exact correlations in a single file system with a driven tracer

Abstract

We study the effect of a single driven tracer particle in a bath of other particles performing the random average process on an infinite line using a stochastic hydrodynamics approach. We consider arbitrary fixed as well as random initial conditions and compute the two-point correlations. For quenched uniform and annealed steady state initial conditions we show that in the large time $T$ limit the fluctuations and the correlations of the positions of the particles grow subdiffusively as $\sqrt{T}$ and have well defined scaling forms under proper rescaling of the labels. We compute the corresponding scaling functions exactly for these specific initial configurations and verify them numerically. We also consider a non translationally invariant initial condition with linearly increasing gaps where we show that the fluctuations and correlations grow superdiffusively as $T^{3/2}$ at large times.

7 pages, 4 figures, supplementary material appended. To appear in EPL

References in corpus (29)

• Macroscopic fluctuation theory
• A Model for Force Fluctuations in Bead Packs
• Macroscopic fluctuation theory for stationary non equilibrium states
• Wealth Distributions in Models of Capital Exchange
• Single-File Diffusion of Atomic and Colloidal Systems: Asymptotic Laws
• Enhanced reaction kinetics in biological cells
• Pushing off the walls: a mechanism of cell motility in confinement
• From random walk to single-file diffusion
• Large Deviations in Single File Diffusion
• Single-File diffusion in a Box
• Theory of Single File Diffusion in a Force Field
• Geometry-induced superdiffusion in driven crowded systems
• Journey of an intruder through the fluidisation and jamming transitions of a dense granular media
• The Lasting Effect of Initial Conditions on Single File Diffusion
• Motion of a driven tracer particle in a one-dimensional symmetric lattice gas
• Diffusion of Finite-Sized Hard-Core Interacting Particles In a One-Dimensional Box - Tagged Particle Dynamics
• Universal Large Deviations for the Tagged Particle in Single File Motion
• Colloids dragged through a polymer solution: experiment, theory and simulation
• Diffusion of Tagged Particle in an Exclusion Process
• Asymmetric particle systems on R
• Tagged Particle Correlations in the Asymmetric Simple Exclusion Process: Finite Size Effects
• Exact Tagged Particle Correlations in the Random Average Process
• Diffusion of a sphere in a dilute solution of polymer coils
• Biased diffusion in a one-dimensional adsorbed monolayer
• Correlation and fluctuation in Random Average Process on an infinite line with a driven tracer
• Dynamics of a driven probe molecule in a liquid monolayer
• Statistical properties of single-file diffusion front
• Structural Responses of Quasi-2D Colloid Fluids to Excitations Elicited by Nonequilibrium Perturbations
• Tagged particle diffusion in one-dimensional gas with Hamiltonian dynamics

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• Particles confined in arbitrary potentials with a class of finite-ranged interactions
• Dynamics of Run-and-Tumble Particles in Dense Single-File Systems
• Tagged particle in single-file diffusion with arbitrary initial conditions
• Phase transition in a 1d driven tracer model
• From Particle Currents to Tracer Diffusion: Universal Correlation Profiles in Single-File Dynamics
• Macroscopic fluctuations of a driven tracer in the symmetric exclusion process
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• Unbinding transition of probes in single-file systems
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• Tracer dynamics in the active random average process
• Exact fluctuation and long-range correlations in a single-file model under resetting