Dynamical instantons and activated processes in mean-field glass models

Dynamical instantons and activated processes in mean-field glass models

Blog Article

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 NATURAL of a reference local minimum.

We show that the associated dynamical mean-field equations admit Apparel Fabric by the Yard 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.