NON-ABELIAN SYMMETRIES OF STOCHASTIC-PROCESSES - DERIVATION OF CORRELATION-FUNCTIONS FOR RANDOM-VERTEX MODELS AND DISORDERED-INTERACTING PARTICLE-SYSTEMS
G. Schutz et S. Sandow, NON-ABELIAN SYMMETRIES OF STOCHASTIC-PROCESSES - DERIVATION OF CORRELATION-FUNCTIONS FOR RANDOM-VERTEX MODELS AND DISORDERED-INTERACTING PARTICLE-SYSTEMS, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics, 49(4), 1994, pp. 2726-2741
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.