We study analytically a model where particles with hard-core repulsion
diffuse on a finite one-dimensional lattice with space-dependent, asy
mmetric hopping rates. The dynamics are given by the U(q)[SU(2)]-symme
tric Hamiltonian of a generalized anisotropic Heisenberg ferromagnet.
Exploiting this symmetry, we derive exact expressions for various corr
elation functions. In the weakly driven system correlation length xi(s
) and correlation time xi(t) are related by xi(t) - xi(s)2 indicating
a dynamical exponent z = 2 as for symmetric diffusion. But also in str
ongly driven systems with finite density we find correlation functions
with a dynamical exponent z = 2. This is not expected from the finite
-size scaling analysis of the model.