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The basic model of the non-equilibrium low dimensional physics the so-calledtotally asymmetric exclusion process is related to the 'crystalline limit'($q\to\infty$) of the $SU_q(2)$ quantum algebra. Using the quantum inversescattering method we obtain the exact expression for the time-dependentstationary correlation function of the totally asymmetric simple exclusionprocess on a one dimensional lattice with the periodic boundary conditions.

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