Synchronization and collective motion of globally coupled Brownian particles

TL;DR

This paper investigates how globally coupled Brownian particles transition from equilibrium to collective motion states due to velocity alignment interactions, revealing the underlying instability mechanism.

Contribution

It introduces a model of passive Brownian particles with social-like velocity alignment coupling, analyzing the transition to collective motion and the instability mechanism involved.

Findings

Transition from thermal equilibrium to collective motion with increased coupling

Instability driven by competition between collision time and orientation time

Identification of conditions leading to collective behavior

Abstract

In this work, we study a system of passive Brownian (non-self-propelled) particles in two dimensions, interacting only through a social-like force (velocity alignment in this case) that resembles Kuramoto's coupling among phase oscillators. We show that the kinematical stationary states of the system go from a phase in thermal equilibrium with no net flux of particles, to far-from-equilibrium phases exhibiting collective motion by increasing the coupling among particles. The mechanism that leads to the instability of the equilibrium phase relies on the competition between two time scales, namely, the mean collision time of the Brownian particles in a thermal bath and the time it takes for a particle to orient its direction of motion along the direction of motion of the group.