Dynamic scaling in the spatial distribution of persistent sites

G. Manoj; P. Ray

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arXiv · cond-mat/9901130

Dynamic scaling in the spatial distribution of persistent sites

G. Manoj·P. Ray

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Abstract

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 $n(k,t)\sim t^{-θ}k^{-τ}f(k/t^{z})$. The new exponents $τ$ and $z$ change with the initial particle density $n_{0}$, and are related to the persistence exponent $θ$ through the scaling relation $z(2-τ)=θ$. We show by rigorous analytic arguments that for all $n_{0}$, $1< τ< 2$, which is confirmed by numerical results.

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G. Manoj, P. Ray. 1999-01-14. Dynamic scaling in the spatial distribution of persistent sites. https://arxiv.org/abs/cond-mat/9901130

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