Boundary crossover in non-equilibrium growth processes

TL;DR

This paper investigates how boundaries affect the growth and roughness of stochastic interfaces in non-equilibrium processes, revealing a universal scaling behavior near boundaries through analytical and numerical methods.

Contribution

It introduces a universal scaling form for local height profiles near boundaries in non-equilibrium growth models, supported by exact solutions and simulations.

Findings

Boundary effects increase interface roughness near the boundary

Universal scaling form for local height profiles is proposed

Exact solutions and simulations confirm the crossover behavior

Abstract

The growth of stochastic interfaces in the vicinity of a boundary and the non-trivial crossover towards the behaviour deep in the bulk is analysed. The causal interactions of the interface with the boundary lead to a roughness larger near to the boundary than deep in the bulk. This is exemplified in the semi-infinite Edwards-Wilkinson model in one dimension, both from its exact solution and numerical simulations, as well as from simulations on the semi-infinite one-dimensional Kardar-Parisi-Zhang model. The non-stationary scaling of interface heights and widths is analyzed and a universal scaling form for the local height profile is proposed.