Singular Scaling Functions in Clustering Phenomena

TL;DR

This paper investigates clustering behaviors in particles sliding on fluctuating surfaces, revealing singular scaling functions and giant fluctuations, with similarities to particles in quenched disordered environments.

Contribution

It introduces the concept of singular scaling functions in clustering phenomena and compares dynamic behaviors in fluctuating and frozen surface systems.

Findings

Scaling functions exhibit cusp and divergence singularities.

Giant fluctuations persist in the thermodynamic limit.

Similarities found between fluctuating and quenched surface systems.

Abstract

We study clustering in a stochastic system of particles sliding down a fluctuating surface in one and two dimensions. In steady state, the density-density correlation function is a scaling function of separation and system size.This scaling function is singular for small argument -- it exhibits a cusp singularity for particles with mutual exclusion, and a divergence for noninteracting particles. The steady state is characterized by giant fluctuations which do not damp down in the thermodynamic limit. The autocorrelation function is a singular scaling function of time and system size. The scaling properties are surprisingly similar to those for particles moving in a quenched disordered environment that results if the surface is frozen.