Effects of environmental heterogeneity and self-propulsion on diffusion crossover of active matter

The crossover from anomalous to normal diffusion in active matter systems is ubiquitous. For future envisioned applications of active matter, understanding their behavior in heterogeneous environments is critical. However, the effects of environmental heterogeneity and self-propulsion on crossover dynamics remain unclear. Here, we introduce a model of self-propelled particles in heterogeneous diffusivity landscapes that exhibits subdiffusive–diffusive crossovers. Each particle propels itself with a speed and orientation undergoing Brownian dynamics governed by rotational diffusion coefficient. In regimes of high rotational diffusion coefficient, we derive a scaling law for critical crossover timescale in terms of self-propulsion parameters and spatial fluctuations strength of heterogeneous diffusivity, validated through simulations. Furthermore, orientational persistence effects, absent in high rotational diffusion coefficient regimes, significantly reduce critical crossover timescales. In low rotational diffusion coefficient regimes, strong orientational persistence with environmental heterogeneity suppresses critical crossover timescales by an order of magnitude compared with orientational persistence-free scenarios. These findings establish a quantitative framework for analyzing how self-propulsion regulates diffusion crossover in heterogeneous environments, with potential implications to synthetic active colloids.