In mathematical physics, the ODE/IM correspondence is a link between ordinary differential equations (ODEs) and integrable models. It was first found in 1998 by Patrick Dorey and Roberto Tateo.[1] In this original setting it relates the spectrum of a certain integrable model of magnetism known as the XXZ-model to solutions of the one-dimensional Schrödinger equation with a specific choice of potential, where the position coordinate is considered as a complex coordinate.
Since then, such a correspondence has been found for many more ODE/IM pairs.[2]
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References edit
- ^ Dorey, Patrick; Tateo, Roberto (24 September 1999). "Anharmonic oscillators, the thermodynamic Bethe ansatz and nonlinear integral equations". Journal of Physics A: Mathematical and General. 32 (38): L419–L425. arXiv:hep-th/9812211. doi:10.1088/0305-4470/32/38/102.
- ^ Dorey, Patrick; Dunning, Clare; Tateo, Roberto (10 August 2007). "The ODE/IM correspondence". Journal of Physics A: Mathematical and Theoretical. 40 (32): R205–R283. arXiv:hep-th/0703066. doi:10.1088/1751-8113/40/32/R01. S2CID 14281617.