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Dynamical Instantons and Activated Processes in Mean-Field Glass Models

by V. Ros, G. Biroli, C. Cammarota

Submission summary

As Contributors: Valentina Ros
Arxiv Link: https://arxiv.org/abs/2006.08399v2 (pdf)
Date submitted: 2020-07-08 02:00
Submitted by: Ros, Valentina
Submitted to: SciPost Physics
Discipline: Physics
Subject area: Statistical and Soft Matter Physics
Approach: Theoretical

Abstract

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 high-dimensional 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 barrier-crossing. Finally, using time-reversal transformations, we construct the two-point function dynamical instanton of the corresponding activated process.

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Submission 2006.08399v2 on 8 July 2020

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