### Abstract

Edwards-Wilkinson type models are studied in 1+1 dimensions and the time-dependent distribution [Formula Presented]([Formula Presented],t) of the square of the width of an interface [Formula Presented] is calculated for systems of size L. We find that, using a flat interface as an initial condition, [Formula Presented]([Formula Presented],t) can be calculated exactly and it obeys scaling in the form 〈[Formula Presented][Formula Presented][Formula Presented]([Formula Presented],t)=Φ([Formula Presented]/〈[Formula Presented][Formula Presented],t/ [Formula Presented]), where 〈[Formula Presented][Formula Presented] is the stationary value of [Formula Presented]. For more complicated initial states, scaling is observed only in the large-time limit and the scaling function depends on the initial amplitude of the longest wavelength mode. The short-time limit is also interesting since [Formula Presented]([Formula Presented],t) is found to closely approximate the log-normal distribution. These results are confirmed by Monte Carlo simulations on a single-step, solid-on-solid type model (roof-top model) of surface evolution.

Original language | English |
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Pages (from-to) | 2256-2260 |

Number of pages | 5 |

Journal | Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics |

Volume | 54 |

Issue number | 3 |

DOIs | |

Publication status | Published - Jan 1 1996 |

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### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics
- Condensed Matter Physics
- Physics and Astronomy(all)