Survival in equilibrium step fluctuations

C. Dasgupta 1, M. Constantin 1, 2, S. Das Sarma 1, Satya N. Majumdar 3

Physical Review E: Statistical, Nonlinear, and Soft Matter Physics 69 (2004) 022101

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.

  • 1. Condensed Matter Theory Center, Department of Physics,
    University of Maryland at College Park
  • 2. Materials Research Science and Engineering Center, Department of Physics,
    University of Maryland at College Park
  • 3. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS),
    CNRS : UMR8626 – Université Paris XI - Paris Sud