Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 6 (2010), 039, 15 pages      arXiv:1005.1988      https://doi.org/10.3842/SIGMA.2010.039
Contribution to the Proceedings of the XVIIIth International Colloquium on Integrable Systems and Quantum Symmetries

Dynamical Critical Exponent for Two-Species Totally Asymmetric Diffusion on a Ring

Birgit Wehefritz-Kaufmann
Department of Mathematics and Physics, Purdue University, 150 N. University Street, West Lafayette, IN 47906, USA

Received September 28, 2009, in final form April 30, 2010; Published online May 12, 2010

Abstract
We present a study of the two species totally asymmetric diffusion model using the Bethe ansatz. The Hamiltonian has Uq(SU(3)) symmetry. We derive the nested Bethe ansatz equations and obtain the dynamical critical exponent from the finite-size scaling properties of the eigenvalue with the smallest real part. The dynamical critical exponent is 3/2 which is the exponent corresponding to KPZ growth in the single species asymmetric diffusion model.

Key words: asymmetric diffusion; nested Uq(SU(3)) Bethe ansatz; dynamical critical exponent.

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