Mode-coupling theory for active Brownian particles

We present a mode-coupling theory (MCT) for the slow dynamics of two-dimensional spherical active Brownian particles (ABPs). The ABPs are characterized by a self-propulsion velocity v(0) and by their translational and rotational diffusion coefficients D-t and D-r, respectively. Based on the integration-through-transients formalism, the theory requires as input only the equilibrium static structure factors of the passive system (where v(0) = 0). It predicts a nontrivial idealized-glass-transition diagram in the three-dimensional parameter space of density, self-propulsion velocity, and rotational diffusivity that arise because at high densities, the persistence length of active swimming l(p) = v(0)/D-r interferes with the interaction length l(c) set by the caging of particles. While the low-density dynamics of ABPs is characterized by a single Peclet number Pe = v(0)(2)/DrDt, close to the glass transition the dynamics is found to depend on Pe and l(p) separately. At fixed density, increasing the self-propulsion velocity causes structural relaxation to speed up, while decreasing the persistence length slows down the relaxation. The active-MCT glass is a nonergodic state that is qualitatively different from the passive glass. In it, correlations of initial density fluctuations never fully decay, but also an infinite memory of initial orientational fluctuations is retained in the positions.