# Survival in equilibrium step fluctuations

Source: [Survival in equilibrium step fluctuations](<https://www.sota2.com/research/paper/68fa1e597a2b558e29321dc0>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-23T14:52:47.983Z

Authors: C. Dasgupta, M. Constantin, S. Das Sarma, Satya N. Majumdar

Published: 2003-07-03T19:24:06.000Z

## 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.

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/cond-mat/0307086>)

[PDF](<https://arxiv.org/pdf/cond-mat/0307086.pdf>)