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Dynamical instantons and activated processes in mean-field glass models

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Valentina Ros, Giulio Biroli, Chiara Cammarota

Original languageEnglish
Article number002
JournalSciPost Physics
Issue number1
Published4 Jan 2021

Bibliographical note

Funding Information: Funding information This work is supported by the Simons Foundation collaboration Cracking the Glass Problem (No. 454935 to G. Biroli). V.Ros acknowledges funding by the LabEx ENS-ICFP: ANR-10-LABX-0010/ANR-10-IDEX-0001-02 PSL* Publisher Copyright: Copyright © 2021 V. Ros et al. Copyright: Copyright 2021 Elsevier B.V., All rights reserved.


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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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