Giant Kovacs-Like Memory Effect for Active Particles

Dynamical properties of self-propelled particles obeying a bounded confidence rule are investigated by means of kinetic theory and agent-based simulations. While memory effects are 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.

Figure 1

The relaxation curve ${\mathrm{\Psi }}_{1f}(t)$ (dash-dotted line) and the Kovacs hump $\mathrm{\Psi }(t)$ (solid red line) obtained from the kinetic theory (1) are in good agreement with agent-based simulations (light green squares and light red circles, respectively). The linear theory (2) (dashed black line) describes the Kovacs effect well for short $t_w=8$. System parameters are $\alpha =0.47\pi$, $M=0.2$, ${\eta }_1=0.3797$, ${\eta }_2=0.4553$, ${\eta }_f=0.3940$ [49]. The lower part shows the noise strength according to the Kovacs protocol.

Figure 2

The relaxation curves ${\mathrm{\Psi }}_{1f}(t)$, ${\mathrm{\Psi }}_{2f}(t)$ (dash-dotted line) and the Kovacs hump $\mathrm{\Psi }(t)$ (solid red line) obtained from the kinetic theory (1) are in good agreement with agent-based simulations (light green squares and light red circles, respectively). The linear theory (2) (dashed black line) fails to describe the Kovacs hump whereas the nonlinear theory (7) with time shift $\widehat{t}=332$ (dotted blue line) agrees well. Parameters are $\alpha =0.35\pi$, $M=0.2$, $t_w=745$, ${\eta }_1=0.3354$, ${\eta }_2=0.2017$, ${\eta }_f=0.2884$ [49].

Figure 3

Anomalous Kovacs effect for a driven granular gas. The order parameter $\beta$ is related to the granular temperature. Displayed are relaxation curves (green dash-dotted lines) and the Kovacs hump (red solid line). The Kovacs effect is very small and shown in the inset in units of ${10}^{-2}$. The nonlinear theory (blue dotted line), Eq. (7) with $\widehat{t}=0$, describes the anomalous effect well; the linear theory (black dashed line), Eq. (2), fails. Details on the data are given in Ref. [48].