NON-ABELIAN SYMMETRIES OF STOCHASTIC-PROCESSES - DERIVATION OF CORRELATION-FUNCTIONS FOR RANDOM-VERTEX MODELS AND DISORDERED-INTERACTING PARTICLE-SYSTEMS

We consider systems of particles hopping stochastically on d-dimension al lattices with space-dependent probabilities. We map the master equa tion onto an evolution equation in a Fock space where the dynamics are given by a quantum Hamiltonian (continuous time) or a transfer matrix (discrete time). Using non-Abelian symmetries of these operators we d erive duality relations, expressing the time evolution of a given init ial configuration in terms of correlation functions of simpler dual pr ocesses. Particularly simple results are obtained for the time evoluti on of the density profile. As a special case we show that for any SU(2 ) symmetric system the two-point and three-point density correlation f unctions in the N-particle steady state can be computed from the proba bility distribution of a single particle moving in the same environmen t. We apply our results to various models, among them partial exclusio n, a simple diffusion-reaction system, and the two-dimensional six-ver tex model with space-dependent vertex weights. For a random distributi on of the vertex weights one obtains a version of the random-barrier m odel describing diffusion of particles in disordered media. We derive exact expressions for the averaged two-point density correlation funct ions in the presence of weak, correlated disorder.