Sign-time distributions for interface growth

TL;DR

This paper studies the sign-time distributions in interface growth, revealing a new critical dimension and unifying persistence properties across various growth processes through analytical and numerical methods.

Contribution

It introduces a unified framework for analyzing sign-time distributions in interface growth, identifying a new critical dimension and characterizing different growth mechanisms.

Findings

Existence of a non-trivial scaling relation.

Identification of a new critical dimension.

Numerical simulations illustrating diverse DST types.

Abstract

We apply the recently introduced distribution of sign-times (DST) to non-equilibrium interface growth dynamics. We are able to treat within a unified picture the persistence properties of a large class of relaxational and noisy linear growth processes, and prove the existence of a non-trivial scaling relation. A new critical dimension is found, relating to the persistence properties of these systems. We also illustrate, by means of numerical simulations, the different types of DST to be expected in both linear and non-linear growth mechanisms.