REACTION-DIFFUSION PROCESSES OF HARD-CORE PARTICLES

We study a 12-parameter stochastic process involving particles with tw o-site interaction and hard-core repulsion on a d-dimensional lattice. In this model, which includes the asymmetric exclusion process, conta ct processes, and other processes, the stochastic variables are partic le occupation numbers taking values n(x) = 0, 1. We show that on a ten -parameter submanifold the k-point equal-time correlation functions [n (x1) ... n(xk)] satisfy linear differential-difference equations invol ving no higher correlators. In particular, the average density [n(x)] satisfies an integrable diffusion-type equation. These properties are explained in terms of dual processes and various duality relations are derived. By defining the time evolution of the stochastic process in terms of a quantum Hamiltonian H, the model becomes equivalent to a la ttice model in thermal equilibrium in d + 1 dimensions. We show that t he spectrum of H is identical to the spectrum of the quantum Hamiltoni an of a d-dimensional, anisotropic, spin-1/2 Heisenberg model. In one dimension our results hint at some new algebraic structure behind the integrability of the system.