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

The basic model of the non-equilibrium low dimensional physics the so-called totally asymmetric exclusion process is related to the ‘crystalline limit’ ($q\to \mathrm{\infty }$) of the $S{U}_q(2)$ 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.