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].