Dynamic fluctuations of elastic lines in random environments

TL;DR

This paper investigates the two-time global roughness fluctuations of finite elastic lines in random environments, proposing a scaling form that captures temperature, size, and aging effects, with implications for non-equilibrium systems.

Contribution

It introduces a novel scaling form for the roughness distribution of elastic lines, accounting for two-time, temperature, and size dependencies, and explores its relevance to non-equilibrium phenomena.

Findings

Fluctuations resemble Edwards-Wilkinson interface at high temperature.

Scaling function varies with aging and proximity to saturation.

Results may apply to other non-equilibrium critical systems.

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.