Spatial survival probability for one-dimensional fluctuating interfaces in the steady state
Abstract
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 steady-state profiles generated by integrating a spatially discretized form of the Edwards-Wilkinson equation to long times. We show that the survival probability exhibits scaling behavior in its dependence on the system size and the `sampling interval' used in the measurement for both `steady-state' and `finite' initial conditions. Analytic results for the scaling functions are obtained from a path-integral treatment of a formulation of the problem in terms of one-dimensional Brownian motion. A `deterministic approximation' is used to obtain closed-form expressions for survival probabilities from the formally exact analytic treatment. The resulting approximate analytic results provide a fairly good description of the numerical data.
Cite
@article{arxiv.cond-mat/0509109,
title = {Spatial survival probability for one-dimensional fluctuating interfaces in the steady state},
author = {Satya N. Majumdar and Chandan Dasgupta},
journal= {arXiv preprint arXiv:cond-mat/0509109},
year = {2009}
}
Comments
RevTeX4, 21 pages, 8 .eps figures, changes in sections IIIB and IIIC and in Figs 7 and 8, version to be published in Physical Review E