Atomic diffusion, step relaxation, and step fluctuations

We show that the dynamics of the pair correlation function in a step train can pinpoint the dominant relaxation mechanism occurring at a crystal surface. Evaporation-condensation and step-edge diffusion do not produce dynamical correlations between neighboring steps, while terrace diffusion may lead to correlations which fall off like a power law with distance and which are peaked at a characteristic time. We derive these results within a "real space'' Langevin formalism which is based on diffusion kernels which are different for each mass transport process. We validate this formalism by reproducing the step fluctuation autocorrelation function. We then derive results on the pair correlation between different steps. Results for solvable limiting cases are summarized in Tables I and II of the paper. As an intermediate step in the analysis we also find expressions for the relaxation time tau(pq) of a mode of wave number q along the steps and wave number p perpendicular to the steps, which we also discuss and compare with prior work. [S1063-651X(99)06907-X].