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

Abstract

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 scattering 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.

Kinetic roughening, global quantities, and fluctuation–dissipation relations

“…Quite some attention was paid recently to the ageing processes [14] that take place during the correlated growth regime [15,16,17,18,19,20,21,22,23]. Most of the studies focused on local quantities as for example the height-height correlation function, ‡ In the following we mostly use the language of growth processes, but due to the different physical situations described by the same Langevin equations our results have a broader range of applications.…”

“…the response of the height to a local perturbation, the two-time roughness or the twotime incoherent scattering function [15,16,17,18,19,20]. In [21] we discussed the correlation function of the squared width and the response of the squared width to a global perturbation.…”

From dynamical scaling to local scale-invariance: a tutorial

“…This is exactly solvable and one readily obtains the exact expressions for the height response and correlators, in the frame where h(t, r) = 0 [41,42] R(t, s; r) = δ h(t, r) δj(s, 0) j=0…”

Disordered vortex matter out of equilibrium: a Langevin molecular dynamics study

“…In the context of interacting vortices in a disordered environment an impressive list of twotime quantities has been discussed [6,14,15,[17][18][19][20][21]. Some of these quantities contain information about local thermal fluctuations, whereas others provide insight into the time evolution of the global structure of the flux line configuration.…”