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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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