Abstract
The properties of the generalized survival probability, that is, the probability of not crossing an arbitrary location during relaxation, have been investigated experimentally (via scanning tunneling microscope observations) and numerically. The results confirm that the generalized survival probability decays exponentially with a time constant . The distance dependence of the time constant is shown to be , where is the material-dependent mean-squared width of the step fluctuations. The result reveals the dependence on the physical parameters of the system inherent in the prior prediction of the time constant scaling with , with the system size and the roughness exponent. The survival behavior is also analyzed using a contrasting concept, the generalized inside survival , which involves fluctuations to an arbitrary location further from the average. Numerical simulations of the inside survival probability also show an exponential time dependence, and the extracted time constant empirically shows behavior, with varying over 0.6 to 0.8 as the sampling conditions are changed. The experimental data show similar behavior, and can be well fit with for , and for . Over this temperature range, the ratio of the fixed sampling time to the underlying physical time constant, and thus the true correlation time, increases by a factor of . Preliminary analysis indicates that the scaling effect due to the true correlation time is relevant in the parameter space of the experimental observations.
3 More- Received 11 December 2006
DOI:https://doi.org/10.1103/PhysRevE.76.021601
©2007 American Physical Society