Robert Grossmann
PTB Berlin

On the diffusion properties of active particles and the synchronization of moving oscillators

In the first part of the talk, the diffusion properties of self-propelled particles which move at constant speed and, in addition, reverse their direction of motion repeatedly are investigated. Particles carry internal oscillators (clocks) triggering these reversal events. We derive a general expression for the diffusion coefficient for this model. Our analysis reveals the existence of an optimal, finite rotational noise amplitude which maximizes the diffusion coefficient. We comment on the relevance of this result with regard to microbiological systems. In the second part, we address the question how these 'moving oscillators' can synchronize. In particular, we investigate the crucial influence of the mobility pattern of particles on the transition from incoherence to synchronization. We consider both, normal diffusion and superdiffusive motion. For normally diffusing oscillators, a finite-size scaling analysis reveals a Berezinskii-Kosterlitz-Thouless transition from incoherence to quasi long-range order. In contrast, we show that superdiffusion induces a continuous phase transition to synchronization and long-range order in two dimensions.