Glassy dynamics of athermal self-propelled particles: Computer simulations and a nonequilibrium microscopic theory

We combine computer simulations and analytical theory to investigate the glassy dynamics in dense assemblies of athermal particles evolving under the sole influence of self-propulsion. Our simulations reveal that when the persistence time of the self-propulsion is increased, the local structure becomes more pronounced, whereas the long-time dynamics first accelerates and then slows down. We explain these surprising findings by constructing a nonequilibrium microscopic theory that yields nontrivial predictions for the glassy dynamics. These predictions are in qualitative agreement with the simulations and reveal the importance of steady-state correlations of the local velocities to the nonequilibrium dynamics of dense self-propelled particles.

Figure 1

Evolution of the structure and dynamics with the persistence time ${\tau }_p$ at $T_{\text{eff}}=0.5$ [(a)–(c)] and comparison of dynamics in active systems with ${\tau }_p=2\times {10}^{-3}$ and Brownian systems at $T=T_{\mathrm{eff}}$ [(d)–(f)]. In panels (a) and (b) solid lines correspond to ${\tau }_p=0$ (equivalent to a thermal system at $T=0.5$), and the dashed and dot-dashed lines correspond to ${\tau }_p=2\times {10}^{-3}$ and $2\times {10}^{-2}$, respectively. In panel (a) we show the pair distribution function $g\left(r\right)$; the curves are shifted vertically for clarity. In panel (b) we show the self-intermediate scattering function $F_s(q;t)=\langle e^{i\mathbf{q}·({\mathbf{r}}_j\left(t\right)-{\mathbf{r}}_j\left(0\right))}\rangle$ for $q=7.25$. In panel (c) we show the relaxation time, ${\tau }_{\alpha }$ (circles) and the peak value of $g\left(r\right)$ (triangles). The relaxation time is defined as $F_s(q;{\tau }_{\alpha })=e^{-1}$. In panels (d) and (e) solid lines correspond to active systems at $T_{\text{eff}}=1$, 0.6, 0.45, and 0.4, and dashed lines correspond to equilibrium systems at $T=1$, 0.6, and 0.45 (from left to right). In panel (d) we show mean-square displacement $\langle \delta r^2\left(t\right)\rangle =\langle ({\mathbf{r}}_j\left(t\right)-{\mathbf{r}}_j\left(0\right){)}^2\rangle$, and in panel (e) we show $F_s(q;t)$. In panel (f) circles represent ${\tau }_{\alpha }$, squares represent the inverse self-diffusion coefficient, $0.1/D$ of active (closed symbols) and thermal (open symbols) systems.

Figure 2

Structure (a, b) and dynamics (c) obtained from simulations and predicted by the theory (d) for various ${\tau }_p$ at $T_{\text{eff}}=0.9$ in the one-component LJ system. (a) Pair distribution function $g\left(r\right)$; the curves are shifted vertically for clarity; ${\tau }_p=0,2\times {10}^{-3}$, and $2\times {10}^{-2}$ (bottom to top). In panel (b) thick lines represent ${\omega }_{\parallel }\left(q\right)/{\omega }_{\parallel }\left(\infty \right)$ and thin lines represent $S\left(k\right)$ at ${\tau }_p=2\times {10}^{-4}$ (solid) and $2\times {10}^{-2}$ (dashed). The inset in panel (b) shows the persistence time dependence of ${\omega }_{\parallel }\left(\infty \right){\tau }_p$. In panel (c) we show ${\tau }_{\alpha }$ (circles, left axis) and the peak value of $g\left(r\right)$ (triangles, right axis), obtained from simulations. In panel (d) we show ${\tau }_{\alpha }$ (circles) and the inverse self-diffusion coefficient, $0.1/D$ (squares) predicted by the theory.