Model systems of self-propelled particles reproduce many phenomena observed in laboratory active matter systems that defy our thermal equilibrium-based intuition. In particular, in stationary states of self-propelled systems, it is recognized that velocities of different particles exhibit non-trivial equal-time correlations. Such correlations are absent in equivalent equilibrium systems. Recently, researchers found that the range of the velocity correlations increases with increasing persistence time of the self-propulsion and can extend over many particle diameters. Here we review the initial studies of long-ranged velocity correlations in solid-like systems of self-propelled particles. Then, we demonstrate that the long-ranged velocity correlations are also present in dense fluid-like systems. We show that the range of velocity correlations in dense systems of self-propelled particles is determined by the combination of the self-propulsion and the virial bulk modulus that originates from repulsive interparticle interactions.

自推进粒子模型系统再现了在实验室活性物质系统中观察到的许多现象，这些现象违背了我们基于热平衡的直觉。特别是，在自推进系统的稳态中，人们认识到不同粒子的速度表现出非平凡的等时相关性。这种相关性在等效平衡系统中是不存在的。最近，研究人员发现速度相关性的范围随着自推进持续时间的增加而增加，并且可以扩展到许多粒子直径。在这里，我们回顾了自推进粒子的类固体系统中远程速度相关性的初步研究。然后，我们证明了长程速度相关性也存在于密集的类流体系统中。