The coherent motions of thermal active Brownian particles

Active matter exhibits many intriguing non-equilibrium character, \emph{e.g.}, the active Brownian particles (ABP) without any attractive and aligned interactions can occur the mobility-induced phase transition to form some dense domains with both the structural ordering and dynamical coherence. Recently, the velocity correlation among the particles in the dense and ordered clusters was found in athermal ABP systems, however, seemed to disappear if including the thermal noises to describe microscopic ABPs, bringing some confusion about the generality of the consistence between structure 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 (small) correlation in motions of ABPs. By averaging the instantaneous velocity (or equivalently, calculating the displacement) in various lag times, we show that the motions of thermal-fluctuated ABPs in the one order of magnitude smaller than the translational characteristic time are highly coherent and consistent spatially with the structural ordering of the ABPs.