Survival in equilibrium step fluctuations

TL;DR

This paper combines analytical and numerical methods to study the survival probability in equilibrium step fluctuations, revealing scaling behavior and validating results with experimental STM data.

Contribution

It establishes an exact relation between survival probability and autocorrelation function, and demonstrates scaling behavior in system size and sampling time.

Findings

Exact relation between survival probability and autocorrelation function.

Scaling behavior of survival probability with system size and sampling time.

Agreement of theoretical results with experimental STM data.

Abstract

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.