Stokes Multipliers, Spectral Determinants and T-Q relations
Stokes Multipliers, Spectral Determinants and T-Q relations
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斯托克斯乘数、谱行列式和 T-Q 关系
DOI：
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发表时间：
2000
期刊：
影响因子：
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通讯作者：
J. Suzuki
中科院分区：
文献类型：
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作者：
J. Suzuki
近年来，人们发现了一类常线性微分方程与可积模型之间的显著对应关系。在第一部分中，我们综述了二阶微分方程，具有多项式位势的Schrodinger方程的结果。我们将观察到，在可解模型的研究中，巴克斯特的Q-算子、融合转移矩阵在常微分方程的分析中发挥了重要作用。讲座的第二部分是专门推广到高阶线性微分方程。在二阶常微分方程的情况下发现的对应关系自然被提升。我们还提到了离散孤子理论的一个联系。
Recently, a remarkable correspondence has been unveiled between a certain class of ordi- nary linear differential equations (ODE) and integrable models. In the first part of the report, we survey the results concerningthe 2nd order differential equations, the Schrodinger equa- tion with a polynomial potential. We will observe that fundamental objects in the study of the solvable models, e.g., Baxter's Q− operator, fusion transfer matrices come into play in the analyses on ODE. The second part of the talk is devoted to the generalization to higher order linear differential equations. The correspondence found in the case of the 2nd order ODE is naturally lifted up. We also mention a connection to the discrete soliton theory.