Phenomenology of ageing in the Kardar-Parisi-Zhang equation

TL;DR

This paper investigates the ageing phenomena in surface growth modeled by the 1D KPZ equation, revealing specific ageing exponents and demonstrating the applicability of local scale-invariance to describe autoresponse scaling functions.

Contribution

It provides the first detailed analysis of ageing in the 1D KPZ equation, including the determination of ageing exponents and the validation of a logarithmic local scale-invariance framework.

Findings

Ageing occurs during surface growth with specific exponents a=-1/3, b=-2/3.

Autoresponse functions follow a scaling form described by local scale-invariance.

The dynamical scaling exponent is z=3/2.

Abstract

We study ageing during surface growth processes described by the one-dimensional Kardar-Parisi-Zhang equation. Starting from a flat initial state, the systems undergo simple ageing in both correlators and linear responses and its dynamical scaling is characterised by the ageing exponents a=-1/3, b=-2/3, lambda_C=lambda_R=1 and z=3/2. The form of the autoresponse scaling function is well described by the recently constructed logarithmic extension of local scale-invariance.