Dynamic scaling in the spatial distribution of persistent sites

Details Dynamic scaling in the spatial distribution of persistent sites Dynamic scaling in the spatial distribution of persistent sites

1999-01-14

arxiv.org/abs/cond-mat/9901130v1

Physics

Condensed Matter

Statistical Mechanics

4 pages, REVTEX, 4 postscript figures

Scientific paper

The spatial distribution of persistent (unvisited) sites in one dimensional $A+A\to\emptyset$ model is studied. The `empty interval distribution' $n(k,t)$, which is the probability that two consecutive persistent sites are separated by distance $k$ at time $t$ is investigated in detail. It is found that at late times this distribution has the dynamical scaling form $n(k,t)\sim t^{-\theta}k^{-\tau}f(k/t^{z})$. The new exponents $\tau$ and $z$ change with the initial particle density $n_{0}$, and are related to the persistence exponent $\theta$ through the scaling relation $z(2-\tau)=\theta$. We show by rigorous analytic arguments that for all $n_{0}$, $1< \tau< 2$, which is confirmed by numerical results.

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