Interfaces with a single growth inhomogeneity and anchored boundaries

TL;DR

This paper investigates a one-dimensional growth model with a localized inhomogeneity and anchored boundaries, analyzing its long-term roughening behavior, dynamic scaling, and morphological transitions through exact calculations and numerical studies.

Contribution

It provides an exact calculation of roughening exponents and explores the impact of a localized inhomogeneity on interface dynamics and scaling regimes.

Findings

Exact roughening exponents determined for the stationary regime

Identification of slow morphological transition with vanishing spectral gap

Faceting dynamics observed in gapful situations

Abstract

The dynamics of a one dimensional growth model involving attachment and detachment of particles is studied in the presence of a localized growth inhomogeneity along with anchored boundary conditions. At large times, the latter enforce an equilibrium stationary regime which allows for an exact calculation of roughening exponents. The stochastic evolution is related to a spin Hamiltonian whose spectrum gap embodies the dynamic scaling exponent of late stages. For vanishing gaps the interface can exhibit a slow morphological transition followed by a change of scaling regimes which are studied numerically. Instead, a faceting dynamics arises for gapful situations.