Sampling Time Effects for Persistence and Survival in Step Structural Fluctuations
arXiv:cond-mat/0410094 · doi:10.1103/PhysRevE.71.021602
Abstract
The effects of sampling rate and total measurement time have been determined for single-point measurements of step fluctuations within the context of first-passage properties. Time dependent STM has been used to evaluate step fluctuations on Ag(111) films grown on mica as a function of temperature (300-410 K), on screw dislocations on the facets of Pb crystallites at 320K, and on Al-terminated Si(111) over the temperature range 770K - 970K. Although the fundamental time constant for step fluctuations on Ag and Al/Si varies by orders of magnitude over the temperature ranges of measurement, no dependence of the persistence amplitude on temperature is observed. Instead, the persistence probability is found to scale directly with t/Dt where Dt is the time interval used for sampling. Survival probabilities show a more complex scaling dependence which includes both the sampling interval and the total measurement time tm. Scaling with t/Dt occurs only when Dt/tm is a constant. We show that this observation is equivalent to theoretical predictions that the survival probability will scale as Dt/L^z, where L is the effective length of a step. This implies that the survival probability for large systems, when measured with fixed values of tm or Dt should also show little or no temperature dependence.
27 pages, 10 figures
References in corpus (11)
- Persistence exponents for fluctuating interfaces
- Power and heat fluctuation theorems for electric circuits
- Experimental Persistence Probability for Fluctuating Steps
- Persistence in nonequilibrium surface growth
- Persistence of a Continuous Stochastic Process with Discrete-Time Sampling
- Correlation Time for Step Structural Fluctuations
- Infinite family of persistence exponents for interface fluctuations
- Survival in equilibrium step fluctuations
- Persistence of a Continuous Stochastic Process with Discrete-Time Sampling: Non-Markov Processes
- Distinguishing step relaxation mechanisms via pair correlation functions
- Watching a drunkard for ten nights: A study of distributions of variances
Cited by in corpus (14)
- Universal First-passage Properties of Discrete-time Random Walks and Levy Flights on a Line: Statistics of the Global Maximum and Records
- Universal Asymptotic Statistics of Maximal Relative Height in One-dimensional Solid-on-solid Models
- Symmetry based determination of space-time functions in nonequilibrium growth processes
- Volatility, Persistence, and Survival in Financial Markets
- Spatial survival probability for one-dimensional fluctuating interfaces in the steady state
- Local Persistence in the Directed Percolation Universality Class
- Characterisation of non-equilibrium growth through global two-time quantities
- Dynamic interfaces in an organic thin film
- Persistence and survival in equilibrium step fluctuations
- Controlling Uncertainty of Empirical First-Passage Times in the Small-Sample Regime
- Kinetic roughening, global quantities, and fluctuation-dissipation relations
- Kinetic surface roughening for the Mullins-Herring equation
- Spatial First-passage Statistics of Al/Si(111)-(root3 x root3) Step Fluctuations
- Concentration of Empirical First-Passage Times