Dynamic fluctuations of elastic lines in random environments

Abstract

We study the fluctuations of the two-time dependent global roughness of finite size elastic lines in a quenched random environment. We propose a scaling form for the roughness distribution function that accounts for the two-time, temperature, and size dependence. At high temperature and in the final stationary regime before saturation the fluctuations are as the ones of the Edwards-Wilkinson interface evolving from typical initial conditions. We analyze the variation of the scaling function within the aging regime and with the distance from saturation. We speculate on the relevance of our results to describe the fluctuations of other non-equilibrium systems such as models at criticality.The study of dynamic fluctuations may serve to grasp the nature of non-equilibrium phenomena. Building upon previous analysis of critical static and dynamic fluctuations [1, 2], Rácz [3] proposed to use the scaling functions characterizing the fluctuations of macroscopic -global -observables in non-equilibrium steady states as a classification tool. By introducing 'universality classes' in this way, one could then use them to uncover symmetries and dynamic mechanisms in experimental systems.Another class of non-equilibrium phenomena, including important problems such as glassiness and coarsening, is characterized by a slow relaxation with loss of stationarity [4,5]. It is by now becoming clear that the study of fluctuations [6] is necessary to understand the mechanism for the slowing down and the aging non-equilibrium relaxation in these cases too [7,8].An elastic line under the effect of quenched disorder is a relatively simple system with many aspects of glassiness due to the competition between elasticity and disorder. Its physical realizations are manifold, including interfaces in random ferromagnets [9], crack propagation [10], and vortex lines in high-T c dirty superconductors [11]. The global noise and disorder averaged c EDP Sciences

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

“…7 (b). These results are of the generic form proposed in [9], see equation (26), with α = β EW = 1/2 independently of temperature, ℓ(t) ∼ t 1/2 , and temperature dependencies of the constants made explicit.…”

“…as proposed in [9] for the generic disordered case. Let us list and illustrate in some plots different trends in the scaling function Φ evaluated for the flat initial condition.…”

“…Related models with quenched disorder are problems of elastic manifolds in quenched random environments [8,9,13,16]. In all these studies the finite size dependence was not taken into account and the dynamic fluctuations were not studied.…”

“…In a series of numerical studies one established that, in the numerically accessible times, the quenched dynamics of a disordered 1 + 1 lattice model [8,9] satisfies the scaling in equation (26) with ℓ(t) ∼ t α/ζ and α/ζ a rather small exponent. A crossover to a logarithmic time-dependence [13] is not excluded although it was not seen in the out-of-equilibrium relaxation.…”

“…These works considered only the t w = 0 case with a flat initial condition (T = 0). Recently, a simulation study of a disordered elastic-line model defined on the lattice demonstrated that the scaling form of the distribution function must be modified to include the aging effects [9]. In the body of this Section we analyze the thermal noise-induced dynamic fluctuations of the two-times quantities defined previously during the aging relaxation.…”