Cluster sizes, particle displacements and currents in transport mediated by solitary cluster waves

TL;DR

This paper investigates how solitary cluster waves facilitate particle transport in overdamped systems, revealing a unit displacement law and linking cluster properties to soliton-mediated currents.

Contribution

It introduces a novel unit displacement law for soliton-driven transport and relates cluster sizes to soliton numbers in overdamped particle systems.

Findings

Sum of displacements per soliton equals one wavelength

Derived properties of clusters and their relation to solitons

Quantified particle currents mediated by solitary waves

Abstract

In overdamped particle motion across periodic landscapes, solitary cluster waves can occur at high particle densities and lead to particle transport even in the absence of thermal noise. Here we show that for driven motion under a constant drag, the sum of all particle displacements per soliton equals one wavelength of the periodic potential. This unit displacement law is used to determine particle currents mediated by the solitons. We furthermore derive properties of clusters involved in the wave propagation as well as relations between cluster sizes and soliton numbers.