Effective Edwards-Wilkinson equation for single-file diffusion

Abstract

In this work, we present an effective discrete Edwards-Wilkinson equation aimed to describe the single-file diffusion process. The key physical properties of the system are captured defining an effective elasticity, which is proportional to the single particle diffusion coefficient and to the inverse squared mean separation between particles. The effective equation gives a description of single-file diffusion using the global roughness of the system of particles, which presents three characteristic regimes, namely normal diffusion, subdiffusion and saturation, separated by two crossover times. We show how these regimes scale with the parameters of the original system. Additional repulsive interaction terms are also considered and we analyze how the crossover times depend on the intensity of the additional terms. Finally, we show that the roughness distribution can be well characterized by the Edwards-Wilkinson universal form for the different single-file diffusion processes studied here.

9 pages, 9 figures

References in corpus (13)

• From random walk to single-file diffusion
• Single-File diffusion in a Box
• Width Distributions and the Upper Critical Dimension of KPZ Interfaces
• Theory of Single File Diffusion in a Force Field
• Diffusion of Finite-Sized Hard-Core Interacting Particles In a One-Dimensional Box - Tagged Particle Dynamics
• Langevin formulation for single-file diffusion
• Single file diffusion in macroscopic Wigner rings
• First Passage Distributions in a Collective Model of Anomalous Diffusion with Tunable Exponent
• Dynamic Scaling of Width Distribution in Edwards--Wilkinson Type Models of Interface Dynamics
• Modeling Single-File Diffusion by Step Fractional Brownian Motion and Generalized Fractional Langevin Equation
• Strong Mobility in Weakly Disordered Systems
• Parameter free scaling relation for nonequilibrium growth processes
• Scaling functions for nonequilibrium fluctuations: A picture gallery

Cited by in corpus (13)

• The Lasting Effect of Initial Conditions on Single File Diffusion
• Transition from single-file to two-dimensional diffusion of interacting particles in a quasi-one-dimensional channel
• Single-file escape of colloidal particles from microfluidic channels
• Single File Diffusion of particles with long ranged interactions: damping and finite size effects
• Interacting single-file system: Fractional Langevin formulation versus diffusion-noise approach
• Tunable diffusion of magnetic particles in a quasi-one-dimensional channel
• Calculation of displacement correlation tensor indicating vortical cooperative motion in two-dimensional colloidal liquids
• Insights from Single-File Diffusion into Cooperativity in Higher Dimensions
• Single-File Diffusion of Active Brownian Particles
• Evolution equation for tagged particle density and correlations in single file diffusion
• Scaling laws for single-file diffusion of adhesive particles
• Single-file diffusion on self-similar substrates
• Universal behavior for single-file diffusion on a disordered fractal