  We investigate the influence of external forces on the collective dynamics of
interacting active Brownian particles in two as well as three spatial
dimensions. Via explicit coarse graining, we derive predictive models that are
applicable for space- and time-dependent external force fields. We study these
models for the cases of gravity and harmonic traps. In particular, we derive a
generalized barometric formula for interacting active Brownian particles under
gravity that is valid for low to high concentrations and activities of the
particles. Furthermore, we show that one can use an external harmonic trap to
induce motility-induced phase separation in systems that, without external
fields, remain in a homogeneous state. This finding makes it possible to
realize programmable density patterns in systems of active Brownian particles.
Our analytic predictions are found to be in very good agreement with Brownian
dynamics simulations.
