title: Relaxation after a change in the interface growth dynamics.
abstract: The global effects of sudden changes in the interface growth dynamics are studied using models of the Edwards-Wilkinson (EW) and Kardar-Parisi-Zhang (KPZ) classes during their growth regimes in dimensions d=1 and d=2. Scaling arguments and simulation results are combined to predict the relaxation of the difference in the roughness of the perturbed and the unperturbed interfaces, ΔW^{2}∼s{c}t{-γ}, where s is the time of the change and t>s is the observation time after that event. The previous analytical solution for the EW-EW changes is reviewed and numerically discussed in the context of lattice models, with possible decays with γ=3/2 and γ=1/2. Assuming the dominant contribution to ΔW{2} to be predicted from a time shift in the final growth dynamics, the scaling of KPZ-KPZ changes with γ=1-2β and c=2β is predicted, where β is the growth exponent. Good agreement with simulation results in d=1 and d=2 is observed. A relation with the relaxation of a local autoresponse function in d=1 cannot be discarded, but very different exponents are shown in d=2. We also consider changes between different dynamics, with the KPZ-EW as a special case in which a faster growth, with dynamical exponent z_{i}, changes to a slower one, with exponent z. A scaling approach predicts a crossover time t_{c}∼s{z/z_{i}}≫s and ΔW{2}∼s{c}F(t/t_{c}), with the decay exponent γ=1/2 of the EW class. This rules out the simplified time shift hypothesis in d=2 dimensions. These results help to understand the remarkable differences in EW smoothing of correlated and uncorrelated surfaces, and the approach may be extended to sudden changes between other growth dynamics.
authors.affiliation: Instituto de Física, Universidade Federal da Bahia, Campus Universitário da Federação, Rua Barão de Jeremoabo s/n, 40170-115, Salvador, BA, Brazil.
authors.forename: T A
authors.initials: TA
authors.lastname: de Assis
authors.affiliation: Instituto de Física, Universidade Federal Fluminense, Avenida Litorânea s/n, 24210-340 Niterói RJ, Brazil.
authors.forename: F D A
authors.initials: FD
authors.lastname: Aarão Reis
mesh_terms: D003198:Computer Simulation; D003460:Crystallization / Q000379:methods*; D008956:Models, Chemical; D044367:Phase Transition; D013499:Surface Properties