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Spatial survival probability for one-dimensional fluctuating interfaces in the steady state

Satya N. Majumdar·Chandan Dasgupta
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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.

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BibTeXRIS

Satya N. Majumdar, Chandan Dasgupta. 2005-12-19. Spatial survival probability for one-dimensional fluctuating interfaces in the steady state. https://doi.org/10.1103/physreve.73.011602

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