Path integral approach unveils role of complex energy landscape for activated dynamics of glassy systems

The complex dynamics of an increasing number systems is attributed to the emergence a rugged energy landscape with exponential metastable states. To develop this picture into predictive dynamical theory, I discuss how compute exponentially small probability jump from one state another. This expressed as path integral that can be evaluated by saddle-point methods in mean-field models, leading boundary value problem. resulting equations are solved numerically means Newton-Krylov algorithm paradigmatic spherical $p$-spin glass model invoked diverse contexts supercooled liquids machine-learning algorithms. solutions asymptotic regime large times and physical implications on nature ergodicity-restoring processes.