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

TL;DR

This paper derives an exact expression for the time-dependent stationary correlation function in the totally asymmetric simple exclusion process, linking non-equilibrium physics to quantum algebra via the quantum inverse scattering method.

Contribution

It introduces a determinantal representation of the correlation function for the TASEP using quantum inverse scattering, a novel approach in this context.

Findings

Exact formula for the correlation function obtained

Connection established between TASEP and quantum algebra

Method applicable to periodic boundary conditions

Abstract

The basic model of the non-equilibrium low dimensional physics the so-called totally asymmetric exclusion process is related to the 'crystalline limit' ($q\to\infty$) of the $SU_q(2)$ 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.