Anomalous Diffusion of Active Brownian Particles in Crystalline Phases

Abstract

By performing a molecular-dynamics model of active Brownian particles in 2D geometry and systematically changing the system densities, an investigation of the diffusion of active Brownian particles from homogeneous fluid phases to hexagonal-packed crystalline phases is presented. It is found that particle diffusion is short-time superdiffusive and long-time Fickian, where the effective diffusion coefficient decreases with the increasing density. Such behavior can be theoretically captured by a modified overdamped Langevin equation. On the other hand, the displacement distribution of active Brownian particles in dilute suspensions is identified to be governed by the classic diffusion equation. However, dynamic heterogeneity emerges for the fluctuations of systems in crystalline phases, where the tail of van Hove function is found to follow the exponential distribution instead of the Gaussian form. Such anomalous phenomena perhaps could be attributed to the dense environments where the distribution of particle diffusivity is non-uniform. Our findings potentially provide a significant advance in revealing the fundamental nonequilibrium physics of active matter systems.