Origins of scale invariance in growth processes

TLDR

Scale invariance in far‑from‑equilibrium growth has recently been studied extensively, with a focus on new developments in non‑conserved kinetic roughening. The article aims to develop a comprehensive theory of kinetic surface roughening. The authors analyze solvable needle models illustrating long‑range competition, then treat the two main kinetic roughening classes—Kardar‑Parisi‑Zhang and ideal molecular‑beam‑epitaxy—deriving universality classes and comparing theory to simulations and experiments. For ideal MBE, the study systematically derives universality classes from microscopic processes and shows that continuum theory predictions agree with computer simulations and experimental data.

Abstract

Abstract This review describes recent progress in the understanding of the emergence of scale invariance in far-from-equilibrium growth. The first section is devoted to ‘solvable’ needle models which illustrate the relationship between long-range competition mediated, for example, through shadowing or a Laplacian field, and scale invariance. The following three sections, which comprise the bulk of the article, develop the theory of kinetic surface roughening in a comprehensive manner. The two large classes of kinetic roughening processes, characterized by non-conserved (Kardar-Parisi-Zhang) and conserved (ideal molecular beam epitaxy (MBE)) surface relaxation, respectively, are treated separately. For the former case, which has been extensively reviewed elsewhere, the focus is on recent developments. For the case of ideal MBE we give a systematic derivation of the various universality classes in terms of microscopic processes, and compare the predictions of continuum theory to computer simulations and experiments.