The effect of detachment and attachment to a kink motion in the asymmetric simple exclusion process

TL;DR

This paper investigates how detachment and attachment at various sites influence the movement of a kink in a one-dimensional asymmetric exclusion process, revealing trapping and diffusive behaviors modeled by Fokker-Planck equations.

Contribution

It introduces a theoretical framework describing kink dynamics with attachment/detachment, extending to multiple sites, and validates predictions with Monte Carlo simulations.

Findings

Kink is trapped by a single attachment/detachment site.

Kink exhibits diffusion in a harmonic potential when attachment/detachment occurs at all sites.

Theoretical diffusion constants match Monte Carlo simulation results.

Abstract

We study the dynamics of a kink in a one-lane asymmetric simple exclusion process with detachment and attachment of the particle at arbitrary sites. For a system with one site of detachment and attachment we find that the kink is trapped by the site, and the probability distribution of the kink position is described by the overdumped Fokker-Planck equation with a V-shaped potential. Our results can be applied to the motion of a kink in arbitrary number of sites where detachment and attachment take place. When detachment and attachment take place at every site, we confirm that the kink motion obeys the diffusion in a harmonic potential. We compare our results with the Monte Carlo simulation, and check the quantitative validity of our theoretical prediction of the diffusion constant and the potential form.