  Dynamical properties of a Vicsek-like gas of self-propelled particles are
investigated by means of kinetic theory and agent based simulations. While
memory effects have been observed in disordered systems, we show that they also
occur in active matter systems. In particular, we find that the system exhibits
a giant Kovacs-like memory effect that is much larger than predicted by a
generic linear theory. Based on a separation of time scales we develop a
nonlinear theory to explain this effect. We apply this theory to driven
granular gases and propose further applications to spin glasses.

Statistical Mechanics