17 December 2020
The Random-First-Order-Transition theory of the glass transition stems from the fact that mean-field models of spin-glasses and supercooled liquids display an exponential number of metastable states that trap the dynamics. In order to obtain quantitative dynamical predictions to asses the validity of the theory I discuss how to compute the exponentially small probability that the system jumps from one metastable state to another in a finite time. This is expressed as a path integral that can be evaluated by saddle-point methods in mean-field models, leading to a boundary value problem. The resulting dynamical equations are solved numerically by means of a Newton-Krylov algorithm in the paradigmatic spherical \(p\)-spin glass model. I discuss the solutions in the asymptotic regime of large times and the physical implications on the nature of the ergodicity-restoring processes.