Effective Edwards-Wilkinson equation for single-file diffusion

TL;DR

This paper introduces an effective discrete Edwards-Wilkinson equation to model single-file diffusion, capturing key physical regimes and their scaling, and analyzing the impact of interactions on crossover times and roughness distribution.

Contribution

The work develops a novel effective equation for single-file diffusion that incorporates physical properties and interaction effects, extending the Edwards-Wilkinson framework.

Findings

The effective equation describes normal diffusion, subdiffusion, and saturation regimes.

Crossover times scale with system parameters and interaction strength.

Roughness distribution follows the Edwards-Wilkinson universal form.

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.