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 surfa ce. Evaporation-condensation and step-edge diffusion do not produce dynamic al correlations between neighboring steps, while terrace diffusion may lead to correlations which fall off like a power law with distance and which ar e peaked at a characteristic time. We derive these results within a "real s pace'' Langevin formalism which is based on diffusion kernels which are dif ferent for each mass transport process. We validate this formalism by repro ducing the step fluctuation autocorrelation function. We then derive result s on the pair correlation between different steps. Results for solvable lim iting cases are summarized in Tables I and II of the paper. As an intermedi ate step in the analysis we also find expressions for the relaxation time t au(pq) of a mode of wave number q along the steps and wave number p perpend icular to the steps, which we also discuss and compare with prior work. [S1 063-651X(99)06907-X].