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Residence Time Distribution of Sand Grains in the 1-Dimensional Abelian Sandpile Model

Punyabrata Pradhan·Apoorva Nagar
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Abstract

We study the probability distribution of residence time, $T$, of the sand grains in the one dimensional abelian sandpile model on a lattice of $L$ sites, for $T< >L^2$. The distribution function decays as $\exp(-\frac{K_LT}{L^2})$. We numerically calculate the coefficient $K_L$ for the value of $L$ upto 150 . Interestingly the distribution function has a scaling form $\frac{1}{L^a}f(\frac{T}{L^b})$ with $a \neq b$ for large $L$.

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Punyabrata Pradhan, Apoorva Nagar. 2004-03-31. Residence Time Distribution of Sand Grains in the 1-Dimensional Abelian Sandpile Model. https://arxiv.org/abs/cond-mat/0403769

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