Series expansion for a stochastic sandpile

TL;DR

This paper develops a series expansion method using operator algebra to analyze the activity density in a one-dimensional stochastic sandpile, extending previous perturbation results and providing accurate predictions in the supercritical regime.

Contribution

It introduces an operator algebra-based series expansion approach for stochastic sandpiles, extending the series to higher orders and improving activity predictions.

Findings

Series expanded to O(t^{16})

Predictions match simulations in supercritical regime

Algorithm for operator product expectations

Abstract

Using operator algebra, we extend the series for the activity density in a one-dimensional stochastic sandpile with fixed particle density p, the first terms of which were obtained via perturbation theory [R. Dickman and R. Vidigal, J. Phys. A35, 7269 (2002)]. The expansion is in powers of the time; the coefficients are polynomials in p. We devise an algorithm for evaluating expectations of operator products and extend the series to O(t^{16}). Constructing Pade approximants to a suitably transformed series, we obtain predictions for the activity that compare well against simulations, in the supercritical regime.