Self-organization of self-propulsion forces in a persistent active liquid

We have used Langevin dynamics simulations to study the effects of activity in a two-dimensional dense glass-forming system of Lennard-Jones particles at zero temperature. The activity in this system is characterized by two parameters: the magnitude of the self-propulsion force and its persistence time. We consider the limit of infinite persistence time in which the self-propulsion forces on the particles have the same magnitude but different directions that do not change with time. This system exhibits a liquid state for large values of the self-propulsion force and a force-balanced jammed state if the self-propulsion force is smaller than a threshold value. The average kinetic energy in the liquid state increases with system size, suggesting the presence of long-range correlations. Each particle is found to have a non-zero average velocity in the direction of the self-propulsion force acting on it. A length scale extracted from spatial correlations of the velocity field increases with system size as a power law with exponent close to one. Spatial correlations of the self-propulsion forces also exhibit a similar length scale, indicating that the self-propulsion forces with randomly assigned directions at the beginning of the simulation self-organize to form a steady state in which particles with similar directions of self-propulsion forces come close to one another and move together. This state is “critical” in the sense that it exhibits a correlation length that diverges in the limit of infinite system size.