Active and passive particles: Modeling beads in a bacterial bath

A simple model for the motion of passive beads in a noisy bath of active "boids" interacting only locally is introduced. First, it is shown that under very general assumptions, the beads reproduce the diffusive properties of individual bacteria. Following this, it is argued that the variation of crossover scales observed by Wu and Libchaber (WL) corresponds to the onset of long-range orientational order proven recently to exist in minimal models for collective motion. In this framework, crossover scales are expected to diverge at the critical point and true anomalous diffusion at all scales is then observed.