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Collective dynamics of active Brownian particles in three spatial dimensions: a predictive field theory

We investigate the nonequilibrium dynamics of spherical active Brownian particles in three spatial dimensions that interact via a pair potential. The investigation is based on a predictive local field theory that is derived by a rigorous coarse-graining starting from the overdamped Langevin dynamics of the particles. This field theory is highly accurate and applicable even for the highest activities. It includes configurational order parameters and derivatives up to infinite orders. We present also three finite reduced models that result from the general field theory by suitable approximations and are easier to apply. Furthermore, we use the general field theory and the simplest one of the reduced models to derive analytic expressions for the density-dependent mean swimming speed and the spinodal corresponding to the onset of motility-induced phase separation of the particles, respectively. Both of these results show a good agreement with recent findings described in the literature. The analytic result for the spinodal yields also a prediction for the associated critical point whose position has not been determined before.