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

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

1993-07-14

arxiv.org/abs/cond-mat/9307027v2

Physics

Condensed Matter

10 pages, LATEX

Scientific paper

10.1209/0295-5075/26/1/002

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.

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