Non-trivial activity dependence of static length scale and critical tests of active random first-order transition theory

Effects of activity on glassy dynamics are fundamental in several biological processes. Active glasses extend the scope of the equilibrium problem and provide new control parameters to probe different theoretical aspects. In the theory of glassy dynamics, different length scales play pivotal roles. Here, for the first time, we present results for the static length scale, $\xi_S$, in an active glass via large-scale molecular dynamics simulations for model active glasses in three spatial dimensions. We show that although the relaxation dynamics are equilibrium-like, activity has non-trivial effects on $\xi_S$. $\xi_S$ plays the central role in the random first-order transition (RFOT) theory. Thus, our work provides critical tests for the active RFOT theory, a phenomenological extension of its equilibrium counterpart. We find that the two exponents, $\theta$ and $\psi$, within the theory, become activity-dependent, exposing the non-trivial effects of activity on $\xi_S$. However, the combination of $\theta$ and $\psi$, which controls the relaxation dynamics, remains nearly independent of activity leading to the effectively equilibrium-like behavior. Interestingly, $\xi_S$ shows higher growth in an active glass; this should help better comparison of theories with simulations and experiments.