Passive Sliders and Scaling: from Cusps to Divergences

TL;DR

This paper investigates the steady state behavior of particles sliding on fluctuating surfaces, revealing how clustering and correlations evolve from cusp singularities to divergences through a mapping between different particle systems.

Contribution

It introduces a mapping between systems with mutual exclusion and multiparticle occupancy, demonstrating a transition from cusp to divergence in correlation functions.

Findings

Correlation functions exhibit cusp singularities in one system.

Mapping reveals a transition to divergence in correlations.

Scaling forms are preserved under the mapping.

Abstract

The steady state reached by a system of particles sliding down a fluctuating surface has interesting properties. Particle clusters form and break rapidly, leading to a broad distribution of sizes and large fluctuations. The density-density correlation function is a singular scaling function of the separation and system size. A simple mapping is shown to take a configuration of sliding hard-core particles with mutual exclusion (a system which shows a cusp singularity) to a configuration with multiparticle occupancy. For the mapped system, a calculation of the correlation function shows that it is of the same scaling form again, but with a stronger singularity (a divergence) of the sort observed earlier for noninteracting passive particles.