Out-of-equilibrium relaxation of the Edwards-Wilkinson elastic line

TL;DR

This paper investigates the non-equilibrium relaxation dynamics of the Edwards-Wilkinson elastic line, revealing aging behavior, scaling laws, and fluctuation properties that shed light on broader glassy systems.

Contribution

It provides a detailed analysis of aging, scaling, and fluctuation phenomena in a simple elastic interface model, connecting these to glassy system behaviors.

Findings

Identification of a growing correlation length during relaxation

Generalization of Family-Vicsek scaling to non-equilibrium regimes

Analysis of fluctuation-dissipation theorem violation and its crossover

Abstract

We study the non-equilibrium relaxation of an elastic line described by the Edwards-Wilkinson equation. Although this model is the simplest representation of interface dynamics, we highlight that many (not though all) important aspects of the non-equilibrium relaxation of elastic manifolds are already present in such quadratic and clean systems. We analyze in detail the aging behaviour of several two-times averaged and fluctuating observables taking into account finite-size effects and the crossover to the stationary and equilibrium regimes. We start by investigating the structure factor and extracting from its decay a growing correlation length. We present the full two-times and size dependence of the interface roughness and we generalize the Family-Vicsek scaling form to non-equilibrium situations. We compute the incoherent cattering function and we compare it to the one measured in other glassy systems. We analyse the response functions, the violation of the fluctuation-dissipation theorem in the aging regime, and its crossover to the equilibrium relation in the stationary regime. Finally, we study the out-of-equilibrium fluctuations of the previously studied two-times functions and we characterize the scaling properties of their probability distribution functions. Our results allow us to obtain new insights into other glassy problems such as the aging behavior in colloidal glasses and vortex glasses.