  Active (i.e., self-propelled or swimming) particles moving through an
isotropic fluid exhibit conventional diffusive behavior. We report anomalous
diffusion of an active particle moving in an anisotropic, nematic background.
Whilst the translational motion parallel to the nematic director shows
ballistic behavior, the long-time transverse motion is super-diffusive, with an
anomalous scaling $\propto t \ln t$ of the mean squared displacement with time
$t$. This behavior is predicted by an analytical theory that we present here,
and is corroborated by numerical simulation of active particle diffusion in a
simple lattice model for a nematic liquid crystal. It is universal for any
collection of self-propelled elements (e.g., bacteria or active rods) moving in
a nematic background, provided only that the swimmers are sufficiently dilute
that their interactions with each other can be neglected, and that they do not
perform "hairpin" turns.
