Integrability of two-species partially asymmetric exclusion processes
arXiv:2212.11646 · doi:10.1088/1751-8121/acc55b
Abstract
We work towards the classification of all one-dimensional exclusion processes with two species of particles that can be solved by a nested coordinate Bethe Ansatz. Using the Yang-Baxter equations, we obtain conditions on the model parameters that ensure that the underlying system is integrable. Three classes of integrable models are thus found. Of these, two classes are well known in literature, but the third has not been studied until recently, and never in the context of the Bethe ansatz. The Bethe equations are derived for the latter model as well as for the associated dynamics encoding the large deviation of the currents.
15 pages, 2 figures. Typo in equation (21) corrected. Extra step detail added in Appendix A, case 1, option α=1; Figure A.1 updated accordingly
References in corpus (11)
- The large deviation approach to statistical mechanics
- Non equilibrium steady states: fluctuations and large deviations of the density and of the current
- Nonequilibrium Steady States of Matrix Product Form: A Solver's Guide
- Bethe Ansatz Solution of the Asymmetric Exclusion Process with Open Boundaries
- The asymmetric simple exclusion process: an integrable model for non-equilibrium statistical mechanics
- Construction of a Coordinate Bethe Ansatz for the asymmetric simple exclusion process with open boundaries
- Slowest relaxation mode of the partially asymmetric exclusion process with open boundaries
- Current Fluctuations in the exclusion process and Bethe Ansatz
- Algebraic Bethe Ansatz for the two species ASEP with different hopping rates
- Driven tracers in narrow channels
- Power series method for solving TASEP-based models of mRNA translation