Aging dynamics of non-linear elastic interfaces: the Kardar-Parisi-Zhang equation

TL;DR

This paper investigates the aging dynamics of the (1+1)-dimensional Kardar-Parisi-Zhang equation through numerical simulations, revealing complex aging behavior and scaling properties relevant to glassy dynamics of non-linear elastic interfaces.

Contribution

It provides the first detailed analysis of aging phenomena in the KPZ equation without disorder, identifying scaling laws and distribution functions for the two-times roughness.

Findings

A multiplicative aging scenario for the two-times roughness is observed.

The same growth exponent characterizes both aging and stationary regimes.

The distribution of two-times roughness follows a generalized scaling relation.

Abstract

In this work, the out-of-equilibrium dynamics of the Kardar-Parisi-Zhang equation in (1+1) dimensions is studied by means of numerical simulations, focussing on the two-times evolution of an interface in the absence of any disordered environment. This work shows that even in this simple case, a rich aging behavior develops. A multiplicative aging scenario for the two-times roughness of the system is observed, characterized by the same growth exponent as in the stationary regime. The analysis permits the identification of the relevant growing correlation length, accounting for the important scaling variables in the system. The distribution function of the two-times roughness is also computed and described in terms of a generalized scaling relation. These results give good insight into the glassy dynamics of the important case of a non-linear elastic line in a disordered medium.