Equivalent T-Q relations and exact results for the open TASEP

TL;DR

This paper derives exact eigenvalues for the open TASEP using a simplified T-Q relation, confirming results with the matrix ansatz and extending to conserved charges, advancing understanding of integrable stochastic models.

Contribution

It introduces a simpler T-Q relation for open TASEP, enabling exact computation of eigenvalues and conserved charges, bridging Bethe ansatz and matrix ansatz methods.

Findings

Largest eigenvalue matches matrix ansatz results

Eigenvalues of higher conserved charges computed

Simplified T-Q relation analogous to periodic case

Abstract

Starting from the Bethe ansatz solution for the open Totally Asymmetric Simple Exclusion Process (TASEP), we compute the largest eigenvalue of the deformed Markovian matrix, in exact agreement with results obtained by the matrix ansatz. We also compute the eigenvalues of the higher conserved charges. The key step is to find a simpler equivalent T-Q relation, which is similar to the one for the TASEP with periodic boundary conditions.