Relaxation after a change in the interface growth dynamics
  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, $\Delta W^2 \sim s^c t^{-\gamma}$, 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 $\gamma=3/2$ and $\gamma=1/2$. Assuming the dominant contribution to $\Delta W^2$ to be predicted from a time shift in the final growth dynamics, the scaling of KPZ-KPZ changes with $\gamma = 1-2\beta$ and $c=2\beta$ is predicted, where $\beta$ 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 $t_c\sim s^{z/z_i}\gg s$ and $\Delta W^2 \sim s^c F\left( t/t_c\right)$, with the decay exponent $\gamma=1/2$ 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. 
T. A. de Assis, F. D. A. Aar\~ao Reis
cond-mat.stat-mech