Superdiffusion and diffusion in active matter using a stochastic field theory

One important impact of the out-of-equilibrium nature of active matter is the enhanced fluctuations in the system and the mixing of passive tracers. Interesting properties arise in both small and large concentrations of the active objects. Agent based models can incorporate fluctuations and interactions, but are limited to smaller systems. It can also more difficult to extract physical insight from the results. One of the most successful alternative approaches has been a mean field theory. However, in some situations the mean field theory makes predictions that differ significantly from experiments and direct (agent or particle based) simulations. There are also some quantities that cannot be calculated by the mean field theory. In this talk, we will describe our new approach which uses a stochastic field to overcome the limitations of the mean field assumption. The characteristic superdiffusion observed for passive tracers can be computed along with the longtime diffusivity. We will describe how this enhanced diffusion depends on the characteristics of the active particles and their hydrodynamic interactions.