Generalized Elastic Model: thermal vs non-thermal initial conditions. Universal scaling, roughening, ageing and ergodicity

TL;DR

This paper develops a theoretical framework for the generalized elastic model, revealing universal scaling laws, roughening, ageing, and ergodic properties for systems starting from thermal or non-thermal initial conditions, with implications for experiments.

Contribution

It introduces a comprehensive theoretical approach that broadens previous results and uncovers new scaling behaviors in the correlation functions of the generalized elastic model.

Findings

Universal scaling laws for thermal and non-thermal initial conditions

New correlation function scaling behavior at small times

Comparison of ageing and ergodic properties with continuous time random walk

Abstract

We study correlation properties of the generalized elastic model which accounts for the dynamics of polymers, membranes, surfaces and fluctuating interfaces, among others. We develop a theoretical framework which leads to the emergence of universal scaling laws for systems starting from thermal (equilibrium) or non-thermal (non-equilibrium) initial conditions. Our analysis incorporates and broadens previous results such as observables' double scaling regimes, (super)roughening and anomalous diffusion, and furnishes a new scaling behavior for correlation functions at small times (long distances). We discuss ageing and ergodic properties of the generalized elastic model in non-equilibrium conditions, providing a comparison with the situation occurring in continuous time random walk. Our analysis also allows to assess which observable is able to distinguish whether the system is in or far from equilibrium conditions in an experimental set-up.