$T$-$Q$ relations for the integrable two-species asymmetric simple exclusion process with open boundaries

Abstract

We study the integrable two-species asymmetric simple exclusion process (ASEP) for two inequivalent types of open, non particle conserving boundary conditions. Employing the nested off-diagonal Bethe ansatz method, we construct for each case the corresponding homogeneous $T$-$Q$ relations and obtain the Bethe ansatz equations. Numerical checks for small system sizes show completeness for some Bethe ansatz equations, and partial completeness for others.

arXiv comment30 pages, 7 figures

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Cited by in corpus (4)

• Chiral coordinate Bethe ansatz for phantom eigenstates in the open XXZ spin-$\frac{1}{2}$ chain
• Limiting current distribution for a two species asymmetric exclusion process
• Transition probability and total crossing events in the multi-species asymmetric exclusion process
• Effects of Quantum Pair Creation and Annihilation on a Classical Exclusion Process: the transverse XY model with TASEP