Superdiffusion and antidiffusion in an aligned active suspension

We show theoretically that an imposed uniaxial anisotropy leads to new universality classes for the dynamics of active particles suspended in a viscous fluid. In the homogeneous state, their concentration relaxes superdiffusively, stirred by the long-ranged flows generated by its own fluctuations, as confirmed by our numerical simulations. Increasing activity leads to an anisotropic diffusive instability, and thus an original phase-separation mechanism, driven by the interplay of active stresses with a particle current proportional to the local curvature of the suspension velocity profile.