Spatial first-passage statistics ofAl∕Si(111)−(3×3)step fluctuations

Abstract

The form of the survival probabilities agree quantitatively with the theoretical prediction, which yields exponential decay in the limit of small y/L. The decay constant is found experimentally to be y s /L= 0.076 ± 0

Persistence and first-passage properties in nonequilibrium systems

“…This result has been confirmed [282] in the numerical simulations of the Family model and has also been measured experimentally: for fluctuating step edges in Al/Si(111) system [270] and fluctuating combustion fronts in paper [39]. As in the case of spatial persistence, one can equivalently define [282] the spatial analogue of the temporal survival probability, namely the probability that the interface height h(x, t) stays above its average value 0 over the spatial interval [x 0 , x + x 0 ] along a given direction.…”

“…17). As a result, these systems constitute a beautiful example where many of the theoretical ideas regarding persistence and first-passage properties can be tested experimentally [37,38,270]. For a nice review of the theoretical and experimental results of persistence and first-passage properties of interfaces, particularly in connection to step edges on crystals, see Ref.…”

Persistence and First-Passage Properties in Non-equilibrium Systems

“…For the case of EW or KPZ interfaces in d = 1, we have α = 1/2 and hence θ SS = 1/2 [87]. This result has been confirmed [282] in the numerical simulations of the Family model and has also been measured experimentally: for fluctuating step edges in Al/Si(111) system [270] and fluctuating combustion fronts in paper [39]. As in the case of spatial persistence, one can equivalently define [282] the spatial analogue of the temporal survival probability, namely the probability that the interface height h(x, t) stays above its average value 0 over the spatial interval [x 0 , x + x 0 ] along a given direction.…”

Persistence and survival in equilibrium step fluctuations

“…To obtain these snapshots it is necessary to measure STM images at relatively low temperatures, where step fluctuations are slower than the rate of image acquisition, or to rapidly quench a surface from high temperature so that its step configuration is kinetically frozen [28,48]. Once obtained, spatial STM images provide the step configuration at fixed time, h(x, t 0 ), from which first-passage statistics may be extracted as a function of x. Experimentally determined spatial first-passage statistics have been found [31] to be noisier than the analogous temporal quantities. This arises partially due to the fact that, at large enough length scales along a step edge, there usually exist nonequilibrium features such as forced kinks due to small azimuthal crystal miscut or pinning sites due to trace contamination.…”

“…In this paper, we review the results of our recent analytic, numerical and experimental investigations [20,21,22,23,24,25,26,27,28,29,30,31,32] of various first-passage properties of equilibrium step fluctuations. In these studies, both temporal and spatial persistence and survival probabilities of different kinds are considered and the results of STM experiments on systems with different microscopic mechanisms of step-edge fluctuations are compared directly with the predictions of analytic and numerical calculations for appropriate models.…”