Characterisation of non-equilibrium growth through global two-time quantities

TL;DR

This paper investigates the scaling behavior of global two-time quantities in non-equilibrium growth processes, deriving exact results for linear systems and exploring non-linear effects via numerical simulations, with implications for characterising such systems.

Contribution

It provides exact solutions for linear growth models and analyzes non-linear effects on global quantities, advancing understanding of non-equilibrium growth dynamics.

Findings

Exact expressions for linear Langevin systems like Edwards-Wilkinson.

Numerical analysis of non-linear KPZ equation effects.

Insights into global fluctuation-dissipation ratios.

Abstract

In order to characterise non-equilibrium growth processes, we study the behaviour of global quantities that depend in a non-trivial way on two different times. We discuss the dynamical scaling forms of global correlation and response functions and show that the scaling behaviour of the global response can depend on how the system is perturbed. On the one hand we derive exact expressions for systems characterised by linear Langevin equations (as for example the Edwards-Wilkinson and the noisy Mullins-Herring equations), on the other hand we discuss the influence of non-linearities on the scaling behaviour of global quantities by integrating numerically the Kardar-Parisi-Zhang equation. We also discuss global fluctuation-dissipation ratios and how to use them for the characterisation of non-equilibrium growth processes.