The ODE/IM correspondence

By P. Dorey, C. Dunning, R. Tateo. 2001

259 citations recorded by the source corpus.

This paper reviews a recently discovered link between integrable quantum field theories and certain ordinary differential equations in the complex domain. Along the way, aspects of -symmetric quantum mechanics are discussed, and some elementary features of the six-vertex model and the Bethe ansatz are explained.

Subfields: Atomic and Molecular Physics, and Optics, Geometry and Topology, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/b12e4505fdd77e23e3b3cdaf9e8ec6ba1f70f0d0

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In Atomic and Molecular Physics, and Optics

In Geometry and Topology

In Statistical and Nonlinear Physics

Citations in the corpus

Defects and quantum Seiberg-Witten geometry (2014, background): “• The Calogero-Moser-Sutherland family of integrable models is connected to the Korteweg — de Vries/Benjamin-Ono/Intermediate Long Wave hierarchy [80, 81, 90–93] in the limit of large number of particles.”
Non-Hermitian topology and exceptional-point geometries (2022, background): “(4) are located at z = ±2i, denoted by the red dots in Fig.”
Quantum Geometry and Quiver Gauge Theories (2013, background): “the cluster algebras, the Y - and the T -systems, affine and double affine Hecke algebras [59], knots and three dimensional theories [193], quantum KnizhnikZamolodchikov-Smirnov equation [194–196], affine Toda integrable field theories and many other integrable systems, W -algebras [128, 197], the p”
Observation of PT phase transition in a simple mechanical system (2012, background): “[16, 17] However, as experiments on PT -symmetric physical systems have been performed and published, we have realized that the PT phase transition can be explained simply and intuitively without resorting to sophisticated mathematics.”
T-systems and Y-systems in integrable systems (2010, background): “As a comprehensible review on the ODE/IM correspondence is already available in [149], we only discuss the issue briefly in view of T-system.”
Y-system for scattering amplitudes (2010, unknown): “Similar relations were observed in [38].”