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Abstract: We study the steady state of the abelian sandpile models with stochastictoppling rules. The particle addition operators commute with each other, but ingeneral these operators need not be diagonalizable. We use their abelianalgebra to determine their eigenvalues, and the Jordan block structure. Theseare then used to determine the probability of different configurations in thesteady state. We illustrate this procedure by explicitly determining thenumerically exact steady state for a one dimensional example, for systems ofsize $\le12$, and also study the density profile in the steady state.



Autor: Tridib Sadhu, Deepak Dhar

Fuente: https://arxiv.org/







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