Report on 2006.08399v2

We focus on the energy landscape of simple mean-field models of glasses and analyze activated barrier-crossing by combining the Kac-Rice method for highdimensional Gaussian landscapes with dynamical field theory.In particular, we consider Langevin dynamics at low temperature in the energy landscape of the spherical p-spin model.We select as initial condition for the dynamics one of the many unstable index-1 saddles in the vicinity of a reference local minimum.We show that the associated dynamical mean-field equations admit two solutions: one corresponds to falling back to the original reference minimum, and the other to reaching a new minimum past the barrier.By varying the saddle we scan and characterize the properties of such minima reachable by activated barriercrossing.Finally, using time-reversal transformations, we construct the two-point function dynamical instanton of the corresponding activated process.