Scaling and Fractal formation in Persistence

Details Scaling and Fractal formation in Persistence Scaling and Fractal formation in Persistence

1999-12-13

arxiv.org/abs/cond-mat/9912209v1

Physics

Condensed Matter

Statistical Mechanics

10 pages in ReVTeX, 5 .ps figures as separate files

Scientific paper

The spatial distribution of unvisited/persistent sites in $d=1$ $A+A\to\emptyset$ model is studied numerically. Over length scales smaller than a cut-off $\xi(t)\sim t^{z}$, the set of unvisited sites is found to be a fractal. The fractal dimension $d_{f}$, dynamical exponent $z$ and persistence exponent $\theta$ are related through $z(1-d_{f})=\theta$. The observed values of $d_{f}$ and $z$ are found to be sensitive to the initial density of particles. We argue that this may be due to the existence of two competing length scales, and discuss the possibility of a crossover at late times.

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