Steady State of Stochastic Sandpile Models |
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Authors: | Tridib Sadhu and Deepak Dhar |
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Institution: | (1) Department of Theoretical Physics, Tata Institute of Fundamental Research, Homi Bhaba Road, Mumbai, 400005, India |
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Abstract: | We study the steady state of the Abelian sandpile models with stochastic toppling rules. The particle addition operators commute
with each other, but in general these operators need not be diagonalizable. We use their Abelian algebra to determine their
eigenvalues, and the Jordan block structure. These are then used to determine the probability of different configurations
in the steady state. We illustrate this procedure by explicitly determining the numerically exact steady state for a one dimensional
example, for systems of size ≤12, and also study the density profile in the steady state. |
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Keywords: | Self-organized criticality Stochastic sandpile model |
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