Tao, C. G. ; Cullen, W. G. ; Williams, E. D. ; Dasgupta, C.
(2007)
*Generalized survival in step fluctuations*
Physical Review E - Statistical, Nonlinear and Soft Matter Physics, 76
(2).
021601_1-021601_9.
ISSN 1539-3755

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Official URL: http://pre.aps.org/abstract/PRE/v76/i2/e021601

Related URL: http://dx.doi.org/10.1103/PhysRevE.76.021601

## Abstract

The properties of the generalized survival probability, that is, the probability of not crossing an arbitrary location R 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 Τ_{s}(R). The distance dependence of the time constant is shown to be Τ_{s}(R)=Τ_{s0}exp[-R/w(T)], where w^{2}(T) 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 R/L^{α} , with L the system size and a the roughness exponent. The survival behavior is also analyzed using a contrasting concept, the generalized inside survival S_{in}(t,R), which involves fluctuations to an arbitrary location R further from the average. Numerical simulations of the inside survival probability also show an exponential time dependence, and the extracted time constant empirically shows (R/w)^{λ} behavior, with λ 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 λ=1.0 for T=300 K, and 0.5<λ<1 for T=460 K. 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 -10^{3}. Preliminary analysis indicates that the scaling effect due to the true correlation time is relevant in the parameter space of the experimental observations.

Item Type: | Article |
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Source: | Copyright of this article belongs to The American Physical Society. |

ID Code: | 83260 |

Deposited On: | 17 Feb 2012 04:12 |

Last Modified: | 17 Feb 2012 04:12 |

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