On U_q(SU(2))-symmetric Driven Diffusion

Abstract

We study analytically a model where particles with a hard-core repulsion diffuse on a finite one-dimensional lattice with space-dependent, asymmetric hopping rates. The system dynamics are given by the \mbox{U$_{q}$[SU(2)]}-symmetric Hamiltonian of a generalized anisotropic Heisenberg antiferromagnet. Exploiting this symmetry we derive exact expressions for various correlation functions. We discuss the density profile and the two-point function and compute the correlation length $ξ_s$ as well as the correlation time $ξ_t$. The dynamics of the density and the correlations are shown to be governed by the energy gaps of a one-particle system. For large systems $ξ_s$ and $ξ_t$ depend only on the asymmetry. For small asymmetry one finds $ξ_t \sim ξ_s^2$ indicating a dynamical exponent $z=2$ as for symmetric diffusion.