Exact solution of the one-dimensional deterministic fixed-energy sandpile.
By reason of the strongly nonergodic dynamical behavior, universality properties of deterministic fixed-energy sandpiles are still an open and debated issue. We investigate the one-dimensional model, whose microscopical dynamics can be solved exactly, and provide a deeper understanding of the origin of the nonergodicity. By means of exact arguments, we prove the occurrence of orbits of well-defined periods and their dependence on the conserved energy density. Further statistical estimates of the size of the attraction's basins of the different periodic orbits lead to a complete characterization of the activity vs energy density phase diagram in the limit of large system's size.
Laboratoire de Physique Théorique (UMR du CNRS 8627)--Bâtiment 210, Université de Paris-Sud, 91405 ORSAY Cedex, France.
Luca
L
Dall'Asta