Dynamical instantons and activated processes in mean-field glass models – Archive ouverte HAL

Valentina Ros 1, 2 Giulio Biroli 2 Chiara Cammarota

Valentina Ros, Giulio Biroli, Chiara Cammarota. Dynamical instantons and activated processes in mean-field glass models. SciPost Physics, SciPost Foundation, 2021, 10 (1), ⟨10.21468/SciPostPhys.10.1.002⟩. ⟨hal-03118004⟩

We focus on the energy landscape of a simple mean-field model of glasses and analyze activated barrier-crossing by combining the Kac-Rice method for high-dimensional Gaussian landscapes with dynamical field theory. In particular, we consider Langevin dynamics at low temperature in the energy landscape of the pure 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 barrier-crossing. Finally, using time-reversal transformations, we construct the two-point function dynamical instanton of the corresponding activated process.

  • 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
  • 2. Systèmes Désordonnés et Applications