Driven particle in a cloud of mobile impurities

TL;DR

This paper analyzes the motion of a driven particle interacting with mobile impurities in one dimension, revealing power-law distributions in its excursions and force changes, supported by analytical and numerical methods.

Contribution

It introduces a theoretical and numerical study of a driven particle's dynamics with mobile impurities, highlighting power-law behaviors in one-dimensional systems.

Findings

Distribution of particle excursions scales as a power law with exponent 4/3.

Force change distribution under slow driving also follows a power law with exponent 4/3.

Results are explained using random walk theory.

Abstract

The dynamics of a test particle interacting with diffusing impurities in one dimension is investigated analytically and numerically. In the absence of an applied external force, the dynamics of the particle can be characterized by a distribution of monotonic excursions $\Delta x$, which scales as a power law with an exponent $\tau_{\Delta x} = 4/3$. When the particle is driven at a slow constant velocity, there is again a power law distribution for the monotonic changes of the force $\Delta F$, which is characterized by a similar exponent $\tau_{\Delta F}=4/3$. These results can be understood from the theory of random walks.