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Sfb 288 Differential Geometry and Quantum Physics |
Abstract for Sfb Preprint No. 277
Generalized Knizhnik-Zamolodchikov Equations and Isomonodromy Quantization of the Equations Integrable via the Inverse Scattering Transform: Maxwell-Bloch System with Pumping H. M. Babujian, A. V. Kitaev
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.
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