Non equilibrium dynamics of disordered systems : understanding the broad continuum of relevant time scales via a strong-disorder RG in configuration space

TL;DR

This paper introduces a strong disorder renormalization approach in configuration space to analyze the non-equilibrium dynamics of disordered systems, revealing broad distributions of transition barriers and validating the method with a directed polymer model.

Contribution

The paper develops a novel strong disorder RG method in configuration space for disordered systems' dynamics, applicable to a wide class of models, and demonstrates its effectiveness numerically.

Findings

Distribution of renormalized exit barriers broadens with iteration

Strong disorder RG becomes asymptotically exact at large time scales

Numerical validation with a directed polymer in 2D medium

Abstract

We show that an appropriate description of the non-equilibrium dynamics of disordered systems is obtained through a strong disorder renormalization procedure in {\it configuration space}, that we define for any master equation with transitions rates $W ({\cal C} \to {\cal C}')$ between configurations. The idea is to eliminate iteratively the configuration with the highest exit rate $W_{out} ({\cal C})= \sum_{{\cal C}'} W ({\cal C} \to {\cal C}')$ to obtain renormalized transition rates between the remaining configurations. The multiplicative structure of the new generated transition rates suggests that, for a very broad class of disordered systems, the distribution of renormalized exit barriers defined as $B_{out} ({\cal C}) \equiv - \ln W_{out}({\cal C})$ will become broader and broader upon iteration, so that the strong disorder renormalization procedure should become asymptotically exact at large time scales. We have checked numerically this scenario for the non-equilibrium dynamics of a directed polymer in a two dimensional random medium.