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

SIGMA 5 (2009), 052, 11 pages      arXiv:0904.3680      https://doi.org/10.3842/SIGMA.2009.052
Contribution to the Proceedings of the XVIIth International Colloquium on Integrable Systems and Quantum Symmetries

Determinantal Representation of the Time-Dependent Stationary Correlation Function for the Totally Asymmetric Simple Exclusion Model

Nikolay M. Bogoliubov
St. Petersburg Department of V.A. Steklov Mathematical Institute, Fontanka 27, St. Petersburg 191023, Russia

Received October 30, 2008, in final form April 14, 2009; Published online April 23, 2009

Abstract
The basic model of the non-equilibrium low dimensional physics the so-called totally asymmetric exclusion process is related to the 'crystalline limit' (q → ∞) of the SUq(2) quantum algebra. Using the quantum inverse scattering method we obtain the exact expression for the time-dependent stationary correlation function of the totally asymmetric simple exclusion process on a one dimensional lattice with the periodic boundary conditions.

Key words: quantum inverse method; algebraic Bethe ansatz; asymmetric exclusion process.

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