We report the results of analytic and numerical investigations of the time scale of survival or non-zero-crossing probability S(t) in equilibrium step fluctuations described by Langevin equations appropriate for attachment/detachment and edge-diffusion limited kinetics. An exact relation between long-time behaviors of the survival probability and the autocorrelation function is established and numerically verified. S(t) is shown to exhibit simple scaling behavior as a function of system size and sampling time. Our theoretical results are in agreement with those obtained from an analysis of experimental dynamical STM data on step fluctuations on Al/Si(111) and Ag(111) surfaces.
@article{arxiv.cond-mat/0307086,
title = {Survival in equilibrium step fluctuations},
author = {C. Dasgupta and M. Constantin and S. Das Sarma and Satya N. Majumdar},
journal= {arXiv preprint arXiv:cond-mat/0307086},
year = {2007}
}