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

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 $W(\mathcal{C}\to {\mathcal{C}}^{\prime })$ between configurations. The idea is to eliminate iteratively the configuration with the highest exit rate $W_{out}(\mathcal{C})={\sum }_{{\mathcal{C}}^{\prime }}W(\mathcal{C}\to {\mathcal{C}}^{\prime })$ 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 $B_{out}(\mathcal{C})\equiv -\ln W_{out}(\mathcal{C})$ 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.

v2=final version

References in corpus (2)

• Non-equilibrium relaxation of an elastic string in a random potential
• Non-equilibrium dynamics of polymers and interfaces in random media : conjecture $\psi =d_s/2$ for the barrier exponent

Cited by in corpus (3)

• Equilibrium of disordered systems : constructing the appropriate valleys in each sample via strong disorder renormalization in configuration space
• Non-equilibrium dynamics of finite-dimensional disordered systems : RG flow towards an "infinite disorder" fixed point at large times
• Driven interfaces in random media at finite temperature : is there an anomalous zero-velocity phase at small external force ?