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      Path Integrals for Activated Dynamics in Glassy Systems

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          Abstract

          The Random-First-Order-Transition theory of the glass transition stems from the fact that mean-field models of spin-glasses and supercooled liquids display an exponential number of metastable states that trap the dynamics. In order to obtain quantitative dynamical predictions to asses the validity of the theory I discuss how to compute the exponentially small probability that the system jumps from one metastable state to another in a finite time. This is expressed as a path integral that can be evaluated by saddle-point methods in mean-field models, leading to a boundary value problem. The resulting dynamical equations are solved numerically by means of a Newton-Krylov algorithm in the paradigmatic spherical \(p\)-spin glass model. I discuss the solutions in the asymptotic regime of large times and the physical implications on the nature of the ergodicity-restoring processes.

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          Author and article information

          Journal
          17 December 2020
          Article
          2012.09556

          http://creativecommons.org/licenses/by/4.0/

          Custom metadata
          32 pages, annotated codes in the ancillary files page
          cond-mat.dis-nn cond-mat.soft cond-mat.stat-mech

          Condensed matter, Theoretical physics

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