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 ${\xi }_s$ as well as the correlation time ${\xi }_t$. 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 ${\xi }_s$ and ${\xi }_t$ depend only on the asymmetry. For small asymmetry one finds ${\xi }_t\sim {\xi }_s^2$ indicating a dynamical exponent $z=2$ as for symmetric diffusion.

10 pages, LATEX

References in corpus (4)

• Phase transitions in an exactly soluble one-dimensional exclusion process
• Reaction-Diffusion Processes, Critical Dynamics and Quantum Chains
• Time-dependent correlation functions in a one-dimensional asymmetric exclusion process
• Boundary-Induced Phase Transitions in Equilibrium and Non-Equilibrium Systems

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