Contrasts between coarsening and relaxational dynamics of surfaces

We discuss static and dynamic fluctuations of domain walls separating areas of constant but different slopes in steady-state configurations of crystalline surfaces both by an analytic treatment of the appropriate Langevin equation and by numerical simulations. In contrast to other situations that describe the dynamics in Ising-like systems such as models A and B, we find that the dynamic exponent z=2 that governs the domain wall relaxation function is not equal to the inverse of the exponent n=1/4 that describes the coarsening process that leads to the steady state.