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The persistence behavior for fluctuating steps on the $Si(111)$ $(sqrt3 times sqrt3)R30^{0} - Al$ surface was determined by analyzing time-dependent STM images for temperatures between 770 and 970K. The measured persistence probability follows a power law decay with an exponent of $theta=0.77 pm 0.03$. This is consistent with the value of $theta= 3/4$ predicted for attachment/detachment limited step kinetics. If the persistence analysis is carried out in terms of return to a fixed reference position, the measured persistence probability decays exponentially. Numerical studies of the Langevin equation used to model step motion corroborate the experimental observations.
Numerical and analytic results for the exponent theta describing the decay of the first return probability of an interface to its initial height are obtained for a large class of linear Langevin equations. The models are parametrized by the dynamic r
We report the results of numerical investigations of the steady-state (SS) and finite-initial-conditions (FIC) spatial persistence and survival probabilities for (1+1)--dimensional interfaces with dynamics governed by the nonlinear Kardar--Parisi--Zh
We report numerical and analytic results for the spatial survival probability for fluctuating one-dimensional interfaces with Edwards-Wilkinson or Kardar-Parisi-Zhang dynamics in the steady state. Our numerical results are obtained from analysis of s
We investigate the persistence properties of critical d-dimensional systems relaxing from an initial state with non-vanishing order parameter (e.g., the magnetization in the Ising model), focusing on the dynamics of the global order parameter of a d-
We present a scheme to accurately calculate the persistence probabilities on sequences of $n$ heights above a level $h$ from the measured $n+2$ points of the height-height correlation function of a fluctuating interface. The calculated persistence pr