How non-equilibrium correlations in active matter reveal the topological crossover in glasses

As shown by early studies on mean-field models of the glass transition, the geometrical features of the energy landscape provide fundamental information on the crossover from high-temperature simple relaxational dynamics to low-temperature activated relaxation. In particular, the critical slowing down of dynamics typical of glass formers has been related to a crossover from a saddle-dominated energy landscape (at high temperatures) to a minima-dominated landscape (at low temperatures). We show that active particles can serve as a useful tool to gain insight into this topological crossover. Once configurations equilibrated down in the glassy phase are provided, we show how features of the landscape are revealed by switching on some activity in particle dynamics. In particular we explain here the mechanism, taking as a reference point the pure p-spin model, by which the presence of self-propulsion is expected to induce critical stationary non-equilibrium correlations in correspondence to the minima-to-saddles crossover.