Open 2–TASEP with integrable boundaries

Abstract

In this paper, we explore a two-species extension of the totally asymmetric simple exclusion process (TASEP) known as ‘2–TASEP’ with open boundaries. In this model, carriers on a one-dimensional lattice exhibit distinct behaviors: loaded carriers move right, empty carriers move left, and they exchange positions at a unit rate. At the boundaries carriers are loaded at the left and unloaded at the right. We focus on the stationary state of this model. Using the integrability of this model, we introduce spectral parameters to deform it. This process uncovers an underlying algebraic structure linked to the Weyl group CL . Exploiting this structure, we analytically compute the stationary state of the inhomogeneous model, which permits, after spectral parameter specialization, to derive the exact average particle current of the original 2–TASEP.