Spatial Structures and Giant Number Fluctuations in Models of Active Matter

TL;DR

This paper explores the relationship between giant number fluctuations and structure functions in active matter, revealing a unified classification of models and suggesting experimental ways to detect Porod law violations.

Contribution

It provides a unified framework linking number fluctuations and structure functions across various active matter models, classifying them into four distinct categories.

Findings

Different models fall into four classes based on their structure functions.

Experimental detection of Porod law violation through subleading corrections.

Unified picture connecting density fluctuations and structure functions in active matter.

Abstract

The large scale fluctuations of the ordered state in active matter systems are usually characterised by studying the "giant number fluctuations" of particles in any finite volume, as compared to the expectations from the central limit theorem. However, in ordering systems, the fluctuations in density ordering are often captured through their structure functions deviating from Porod law. In this paper we study the relationship between giant number fluctuations and structure functions, for different models of active matter as well as other non-equilibrium systems. A unified picture emerges, with different models falling in four distinct classes depending on the nature of their structure functions. For one class, we show that experimentalists may find Porod law violation, by measuring subleading corrections to the number fluctuations.