Dynamics of particle deposition on a disordered substrate. II. Far-from-equilibrium behavior

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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 [Phys. Rev. Lett. 56, 889 (1986)]. A generating functional for the correlation and response functions of this process is derived using the approach of Martin, Siggia, and Rose [Phys. Rev. A 8, 423 (1973)]. 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 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 nontrivial crossover effects are found for large intermediate scales.
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