Equilibrium theory for a train of steps was reconsidered by using an analysis which was based upon a non-local Langevin equation that was, in turn, derived from the Burton-Cabrera-Frank model. The Ehrlich-Schwoebel effect, diffusion along step-edges, and elastic interactions between steps were taken into account. An improved estimate was given for the terrace-width distribution. The time dependence of the step fluctuations was calculated by exploiting the dispersion relationship. It was noted that, in the limit of well-separated length-scales, there were several time intervals within which the temporal step correlation function obeyed a power law with an exponent of 1/2, 1/3 or 1/4. In other cases, neither power laws nor simple scaling behaviors were obtained. Precise conditions were defined under which a given regime could be expected in a real situation. It was shown that various physical mechanisms could give rise to the same exponent.

Equilibrium Step Dynamics on Vicinal Surfaces Revisited T.Ihle, C.Misbah, O.Pierre-Louis: Physical Review B, 1998, 58[4], 2289-309