Generalized Knizhnik-Zamolodchikov Equations and Isomonodromy Quantization of the Equations Integrab
Generalized Knizhnik-Zamolodchikov Equations and Isomonodromy Quantization of the Equations Integrab
复制标题
广义Knizhnik-Zamolodchikov方程和方程积分的等单性量化
DOI：
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发表时间：
1998
期刊：
影响因子：
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通讯作者：
A. V. Kitaev
中科院分区：
文献类型：
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作者：
H. Babujian;A. V. Kitaev
通过逆散射变换可积的方程的isomonodromy解的正则量子化导致广义Knizhnik-Zamolodchikov方程。我们可以用离壳的Bethe方法求解这些方程，只要Knizhnik-Zamolodchikov方程与相应李代数的最高权表示相关：这些解可以用超几何型特殊函数的多变量推广来表示。在这项工作中，我们考虑了上述方案的一个实现的Maxwell-Bloch系统的泵：该系统的量子态的多元合流超几何函数。
Canonical quantization of the isomonodromy solutions of equations integrable via the Inverse Scattering Transform leads to generalized Knizhnik–Zamolodchikov equations. One can solve these equations by the off-shell Bethe ansatz method provided the Knizhnik–Zamolodchikov equations are related with the highest weight representations of the corresponding Lie algebras: These solutions can be written in terms of multi-variable generalizations of special functions of the hypergeometric type. In this work, we consider a realization of the above scheme for the Maxwell–Bloch system with pumping: quantum states for this system are found in terms of the multi-variable confluent hypergeometric function.