Singular Scaling Functions in Clustering Phenomena

Details Singular Scaling Functions in Clustering Phenomena Singular Scaling Functions in Clustering Phenomena

2007-10-08

arxiv.org/abs/0710.1494v1

Physics

Condensed Matter

Statistical Mechanics

8 pages, 3 figures, Invited talk delivered at Statphys 23, Genova, July 2007

Scientific paper

10.1140/epjb/e2008-00118-9

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.

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