Journal of Physics A. Mathematical and General vol:24 issue:18 pages:4359-4373
The spatial correlations are investigated for a homogeneous system of indistinguishable particles undergoing stochastic anisotropic hopping dynamics on the d-dimensional lattice, d greater-than-or-equal-to 2. The interaction is zero range, i.e. the rate at which particles leave a given site only depends on the occupation number at that site. A series expansion around the independent particle system is given for the equal time correlations and is shown to converge for small times t. The formal t --> infinity limiting expansion is analysed termwise from which a quadrupole type decay (approximately r(-d)) is derived for the stationary two-points function <eta(0)eta(r)> - <eta(0)>2. This phenomenon of self-organized criticality is a direct consequence of the anisotropy causing the system to violate the condition of detailed balance, combined with the conservation law forcing a diffusive decay (approxiamtely t(-d/2) of the temporal correlations.