Dynamical Instantons and Activated Processes in Mean-Field Glass Models

V. Ros; G. Biroli; C. Cammarota

doi:10.21468/scipostphys.10.1.002

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arXiv · 2006.08399

Dynamical Instantons and Activated Processes in Mean-Field Glass Models

V. Ros·G. Biroli·C. Cammarota

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Abstract

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.

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V. Ros, G. Biroli, C. Cammarota. 2020-06-15. Dynamical Instantons and Activated Processes in Mean-Field Glass Models. https://doi.org/10.21468/scipostphys.10.1.002

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