Diffusion in stochastic sandpiles

Abstract

We study diffusion of particles in large-scale simulations of one-dimensional stochastic sandpiles, in both the restricted and unrestricted versions. The results indicate that the diffusion constant scales in the same manner as the activity density, so that it represents an alternative definition of an order parameter. The critical behavior of the unrestricted sandpile is very similar to that of its restricted counterpart, including the fact that a data collapse of the order parameter as a function of the particle density is only possible over a very narrow interval near the critical point. We also develop a series expansion, in inverse powers of the density. for the collective diffusion coefficient in a variant of the stochastic sandpile in which the toppling rate at a site with $n$ particles is $n(n-1)$, and compare the theoretical prediction with simulation results.

21 pages

References in corpus (1)

• Confirming and extending the hypothesis of universality in sandpiles

Cited by in corpus (8)

• The approach to criticality in sandpiles
• Dynamic correlations in the conserved Manna sandpile
• Anomalous relaxation and hyperuniform fluctuations in center-of-mass conserving systems with broken time-reversal symmetry
• Hydrodynamics, density fluctuations and universality in conserved stochastic sandpiles
• Density relaxation in conserved Manna sandpiles
• Activity, diffusion, and correlations in a two-dimensional conserved stochastic sandpile
• Connecting the Micro-dynamics to the Emergent Macro-variables: Self-Organized Criticality and Absorbing Phase Transitions in the Deterministic Lattice Gas
• Conserved sandpile with a variable height restriction