Reaction-Diffusion Processes of Hard-Core Particles

We study a 12-parameter stochastic process involving particles with two-site interaction and hardcore repulsion on a d-dimensional lattice. In this model, which includes the asymmetric exclusion process, contact processes and other processes, the stochastic variables are particle occupation numbers taking values n~x = 0, 1. We show that on a 10-parameter submanifold the k-point equaltime correlation functions 〈n~x1 · · ·n~xk 〉 satisfy linear differential-difference equations involving 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 lattice model in thermal equilibrium in d + 1 dimensions. We show that the spectrum of H is identical to the spectrum of the quantum Hamiltonian 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.