2003/06/30 by Jurgen F. Stilck, Jürgen F Stilck, Ronald Dickman +2
Computer Science · Mathematics · Physics and Astronomy · #Advanced Mathematical Modeling in Engineering #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #cond-mat.soft #cond-mat.stat-mech
paper · pdf · doi:10.1088/0305-4470/37/4/004
Extended series and improved analysis
arxiv created 2003/10/21 · openalex publication_date 2004/01/09 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
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(t16). Constructing Pade approximants to a suitably transformed series, we obtain predictions for the activity that compare well against simulations, in the supercritical regime.