Noise, diffusion, and hyperuniformity

TL;DR

This paper investigates how particle interactions with center-of-mass conservation influence density fluctuations and hyperuniformity in driven many-particle systems, revealing a balance between noise and deterministic effects at criticality.

Contribution

It introduces a new symmetry in particle models and analyzes its impact on fluctuation decay and hyperuniformity near phase transitions.

Findings

Density fluctuations decay at the fastest rate in the active phase.

Large-scale fluctuations are governed by a balance between noise and deterministic effects.

Results are relevant to shear experiments and understanding hyperuniformity.

Abstract

We consider driven many-particle models which have a phase transition between an active and an absorbing phase. Like previously studied models, we have particle conservation, but here we introduce an additional symmetry - when two particles interact, we give them stochastic kicks which conserve center of mass. We find that the density fluctuations in the active phase decay in the fastest manner possible for a disordered isotropic system, and we present arguments that the large scale fluctuations are determined by a competition between a noise term which generates fluctuations, and a deterministic term which reduces them. Our results may be relevant to shear experiments and may further the understanding of hyperuniformity which occurs at the critical point.