  Biological microswimmers often inhabit a porous or crowded environment such
as soil. In order to understand how such a complex environment influences their
spreading, we numerically study non-interacting active Brownian particles
(ABPs) in a two-dimensional random Lorentz gas. Close to the percolation
transition in the Lorentz gas, they perform the same subdiffusive motion as
ballistic and diffusive particles. However, due to their persistent motion they
reach their long-time dynamics faster than passive particles and also show
superdiffusive motion at intermediate times. While above the critical obstacle
density $\eta_c$ the ABPs are trapped, their long-time diffusion below $\eta_c$
is strongly influenced by the propulsion speed $v_0$. With increasing $v_0$,
ABPs are stuck at the obstacles for longer times. Thus, for large propulsion
speed, the long-time diffusion constant decreases more strongly in a denser
obstacle environment than for passive particles. This agrees with the behavior
of an effective swimming velocity and persistence time, which we extract from
the velocity autocorrelation function.
