Diffusion in stochastic sandpiles

• Published in: The European physical journal. B, Condensed matter physics Condensed matter physics, 2009-12, Vol.72 (3), p.441-449
• Main Authors: da Cunha, S. D., Vidigal, R. R., da Silva, L. R., Dickman, R.
• Format: Article
• Language: English
• Subjects: Classical transport; Complex Systems; Computational methods in statistical physics and nonlinear dynamics; Condensed Matter Physics; Exact sciences and technology; Fluid- and Aerodynamics; Physics; Physics and Astronomy; Solid State Physics; Statistical and Nonlinear Physics; Statistical physics, thermodynamics, and nonlinear dynamical systems; Stochastic analysis methods (fokker-planck, langevin, etc.); Transport processes
• ISSN: 1434-6028; 1434-6036
• DOI: 10.1140/epjb/e2009-00367-0

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 possible, but with a narrow scaling region. 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.