Dynamical density functional theory for the collective behavior of active particles

The collective behavior of active particles represents a fascinating part of nonequilibrium many-body physics with a wealth of phenomena like swarming, activity-induced phase separation and active turbulence. In this contribution we propose an ab initio theory based on the individual active particles (or microswimmers) which is based on the dynamical density functional theory (DDFT) of classical Brownian particles. As an important and nontrivial extension, hydrodynamic interactions between the particles mediated by fluid flow are incorporated such that pushers, pullers and neutral swimmers can be discriminated in the DDFT. As an example, the theory predicts a hydrodynamic pumping state in confined active suspensions both for linear swimmers and circle swimmers which will be proposed and discussed and put into relation with recent experiments.