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In mathematical physics, the Garnier integrable system, also known as the classical Gaudin model is a classical mechanical system discovered by René Garnier in 1919 by taking the 'Painlevé simplification' or 'autonomous limit' of the Schlesinger equations.[1][2] It is a classical analogue to the quantum Gaudin model due to Michel Gaudin[3] (similarly, the Schlesinger equations are a classical analogue to the Knizhnik–Zamolodchikov equations). The classical Gaudin models are integrable.
They are also a specific case of Hitchin integrable systems, when the algebraic curve that the theory is defined on is the Riemann sphere and the system is tamely ramified.
- ^ Garnier, Par M. René (December 1919). "Sur une classe de systèmes différentiels abéliens déduits de la théorie des équations linéaires". Rendiconti del Circolo Matematico di Palermo. 43 (1): 155–191. doi:10.1007/BF03014668. S2CID 120557738.
- ^ Chudnovsky, D. V. (December 1979). "Simplified Schlesinger's systems". Lettere al Nuovo Cimento. 26 (14): 423–427. doi:10.1007/BF02817023. S2CID 122196561.
- ^ Gaudin, Michel (1976). "Diagonalisation d'une classe d'hamiltoniens de spin". Journal de Physique. 37 (10): 1087–1098. doi:10.1051/jphys:0197600370100108700. Retrieved 26 September 2022.