The random growth of interfaces as a subordinated process
Abstract
We study the random growth of surfaces from within the perspective of a single column, namely, the fluctuation of the column height around the mean value, y(t)= h(t)-< h(t)>, which is depicted as being subordinated to a standard fluctuation-dissipation process with friction gamma. We argue that the main properties of Kardar-Parisi-Zhang theory, in one dimension, are derived by identifying the distribution of return times to y(0) = 0, which is a truncated inverse power law, with the distribution of subordination times. The agreement of the theoretical prediction with the numerical treatment of the 1 + 1 dimensional model of ballistic deposition is remarkably good, in spite of the finite size effects affecting this model.
Cite
@article{arxiv.nlin/0407010,
title = {The random growth of interfaces as a subordinated process},
author = {R. Failla and P. Grigolini and M. Ignaccolo and A. Schwettmann},
journal= {arXiv preprint arXiv:nlin/0407010},
year = {2009}
}
Comments
LaTeX, 4 pages, 3 figures