Collective effects in confined Active Brownian Particles

TL;DR

This study reveals that confined active Brownian particles can spontaneously transition from a disordered to a globally rotating state due to finite-size effects, despite lacking explicit inter-particle interactions.

Contribution

It introduces a novel analysis of collective motion in confined active particles, highlighting the role of system size and geometry in emergent behavior without explicit interactions.

Findings

Transition from disordered to ordered rotation observed

Velocity correlation decays algebraically in rotating phase

Global rotation disappears in the infinite system limit

Abstract

We investigate a two-dimensional system of active particles confined to a narrow annular domain. Despite the absence of explicit interactions among the velocities or the active forces of different particles, the system displays a transition from a disordered and stuck state to an ordered state of global collective motion where the particles rotate persistently clockwise or anticlockwise. We describe this behavior by introducing a suitable order parameter, the velocity polarization, measuring the global alignment of the particles' velocities along the tangential direction of the ring. We also measure the spatial velocity correlation function and its correlation length to characterize the two states. In the rotating phase, the velocity correlation displays an algebraic decay that is analytically predicted together with its correlation length while in the stuck regime the velocity correlation decays exponentially with a correlation length that increases with the persistence time. In the first case, the correlation (and, in particular, its correlation length) does not depend on the active force but the system size only. The global collective motion, an effect caused by the interplay between finite-size, periodicity, and persistent active forces, disappears as the size of the ring becomes infinite, suggesting that this phenomenon does not correspond to a phase transition in the usual thermodynamic sense.