# Spatial Organization of Active Particles with Field Mediated Interactions

## TL;DR

This paper investigates how active particles interacting with a fluctuating field and driven by nonequilibrium noise can self-organize into complex spatial patterns, revealing the influence of external driving on pattern formation.

## Contribution

It introduces a model of active particles with internal states and analyzes how nonequilibrium noise influences their spatial organization and phase behavior.

## Key findings

- Identification of a phase diagram with patterned and unpatterned states.
- Demonstration of nonequilibrium drive's role in pattern formation.
- Quantitative analysis of pattern boundary dependence on parameters.

## Abstract

We consider a system of independent point-like particles performing a Brownian motion while interacting with a Gaussian fluctuating background. These particles are in addition endowed with a discrete two-state internal degree of freedom that is subjected to a nonequilibrium source of noise, which affects their coupling with the background field. We explore the phase diagram of the system and pinpoint the role of the nonequilibrium drive in producing a nontrivial patterned spatial organization. We are able, by means of a weakly nonlinear analysis, to account for the parameter-dependence of the boundaries of the phase and pattern diagram in the stationary state.