Survival Probability in the Fluctuations of Interacting Steps

We have performed Monte Carlo studies of survival probabilities $S(t)$ and autocorrelation functions $C(t)$ [1] of interacting steps on vicinal surfaces within the terrace-step-kink (TSK) model. Using Langevin formalism, the analytical and numerical investigations in [1] assumed a step fluctuates in a harmonic confining potential, reminiscent of the Gruber-Mullins model. However, the interaction between steps separated by $\ell$ has the form $A/\ell^2$. Adapting the program written to study distribution of $\ell$ [2], we investigate how $A/\ell ^2$ repulsions alter the relation between long-time behaviors of $S(t)$ and $C(t)$ established in [1]. The ratio of their respective characteristic times decreases as $A$ increases. We also investigate the scaling behavior of $S(t)$ vs.\ system size and sampling time.\\ \noindent [1] C.\ Dasgupta, M.\ Constantin, S.\ Das Sarma, and Satya N.\ Majumdar, Phys.\ Rev.\ E {\bf 69}, 022101 (2004).\\ \noindent [2] Hailu Gebremariam, S.\ D.\ Cohen, H.\ L.\ Richards, and T.\ L.\ Einstein, Phys.\ Rev.\ B {\bf 69}, 125404 (2004).