发表机构
School of Mathematics and Statistics, University of Glasgow（格拉斯哥大学数学与统计学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文通过构造Lax算子证明了变形Toda系统的可积性，展示了其在经典和量子层面的统一性，并给出了n×n Lax矩阵及van Diejen型变形，最后验证了量子代数Bethe ansatz的适用性。
AI 中文摘要
2020年，M. Mucciconi和L. Petrov引入了量子开放非相对论Toda系统的一种长程变形。我们通过构造一个$2 \ imes 2$的Lax算子证明了变形Toda系统的可积性，该算子产生了包含变形Toda系统哈密顿量的交换微分算子族。此外，我们展示了相同的可积变形在经典和量子层面都存在，并且可以应用于非相对论和相对论Toda系统。对于开放非相对论变形Toda系统，我们还给出了一个$n \ imes n$的Lax矩阵，并证明它产生相同的哈密顿量族。我们还展示了如何获得van Diejen型变形Toda系统。最后，我们证明了在量子层面上，代数Bethe ansatz技术可以应用于变形Toda系统。
英文摘要
In 2020 M. Mucciconi and L. Petrov introduced a long-range deformation of the quantum open non-relativistic Toda system. We prove the integrability of the deformed Toda system by constructing a $2 \times 2$ Lax operator, which produces the commutative family of differential operators containing the Hamiltonian of the deformed Toda system. Moreover, we show that the same integrable deformation exists on both classical and quantum levels and can be applied to both non-relativistic and relativistic Toda systems. For the open non-relativistic deformed Toda systems we also present an $n \times n$ Lax matrix and prove that it produces the same family of Hamiltonians. We also show how to obtain the van Diejen-type deformed Toda system. Lastly, we show that on the quantum level the algebraic Bethe ansatz technique can be applied to the deformed Toda system.
Comments25 pages, 2 figures
