The coherent motions of thermal active Brownian particles

Active matter exhibits many intriguing non-equilibrium characteristics, for instance, without any attractive and aligned interactions, the active Brownian particle (ABP) system undergoing motility-induced phase separation forms a high-density phase with both structural ordering and dynamical coherence. Recently, the velocity correlation among the particles in this high-density phase was found in non-thermal overdamped ABP systems. However, it seemed to disappear if thermal noises were included, bringing some confusion about the generality of the consistency between structures and dynamics in ABPs. Here, we demonstrate that the thermal noises imposing a large random term on the instantaneous velocity of ABPs hinder the observation of the inherent correlation in the motions of ABPs. By averaging the instantaneous velocity (or equivalently, calculating the displacement), we show that the inherent motions of thermal-fluctuated ABPs are highly coherent. Whether there is thermal noise or not, the inherent collective motions of ABPs do exist, and the collective motion domains are consistent spatially with the ordered clusters of ABPs in the high-density phase. At the boundary of these ordered clusters, the active forces of the particles tend to point inward and compress to sustain these clusters, thus the particles in the clusters move coherently to form some vortex-like or aligned velocity domains.