Dynamics of Particles Deposition on a Disordered Substrate: II. Far-from Equilibrium Behavior. -

TL;DR

This paper investigates the complex dynamics of particle deposition on disordered substrates, incorporating disorder, periodic potentials, and KPZ growth, revealing that KPZ effects dominate at large scales despite initial disorder influences.

Contribution

It develops a renormalized perturbation theory for a non-equilibrium deposition model including disorder, periodic potential, and KPZ growth, demonstrating renormalizability and large-scale dominance of KPZ behavior.

Findings

Disorder and periodic potential effects decay at large scales.

KPZ term dominates asymptotically.

Strong crossover effects occur at intermediate scales.

Abstract

The deposition dynamics of particles (or the growth of a rigid crystal) on a disordered substrate at a finite deposition rate is explored. We begin with an equation of motion which includes, in addition to the disorder, the periodic potential due to the discrete size of the particles (or to the lattice structure of the crystal) as well as the term introduced by Kardar, Parisi, and Zhang (KPZ) to account for the lateral growth at a finite growth rate. A generating functional for the correlation and response functions of this process is derived using the approach of Martin, Sigga, and Rose. A consistent renormalized perturbation expansion to first order in the non-Gaussian couplings requires the calculation of diagrams up to three loops. To this order we show, for the first time for this class of models which violates the the fluctuation-dissipation theorem, that the theory is renormalizable. We find that the effects of the periodic potential and the disorder decay on very large scales and asymptotically the KPZ term dominates the behavior. However, strong non-trivial crossover effects are found for large intermediate scales.