Diffusive persistence and the `sign-time' distribution
Statistical Mechanics
2009-10-31 v2
Abstract
We present a new method for extracting the persistence exponent theta for the diffusion equation, based on the distribution P of `sign-times'. With the aid of a numerically verified Ansatz for P we derive an exact formula for theta in arbitrary spatial dimension d. Our results are in excellent agreement with previous numerical studies. Furthermore, our results indicate a qualitative change in P above d ~ 36, signalling the existence of a sharp change in the ergodic properties of the diffusion field.
Keywords
Cite
@article{arxiv.cond-mat/9804160,
title = {Diffusive persistence and the `sign-time' distribution},
author = {T. J. Newman and Z. Toroczkai},
journal= {arXiv preprint arXiv:cond-mat/9804160},
year = {2009}
}
Comments
5 pages, 2 tar gzip figures (Latex), subm. to PRE (Rapid Comm), new reference added