The ODE/IM Correspondence

Abstract

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

102 pages, 27 figures. v2: added references

References in corpus (6)

• Pseudo-differential equations, and the Bethe Ansatz for the classical Lie algebras
• Quantization of soliton systems and Langlands duality
• Non-Hermitian Quantum Theory and its Holomorphic Representation: Introduction and Applications
• Solving Baxter's TQ-equation via representation theory
• Schrödinger type eigenvalue problems with polynomial potentials: Asymptotics of eigenvalues
• Non-Hermitian Quantum Theory and its Holomorphic Representation: Introduction and Some Applications

Cited by in corpus (15)

• Three-Hilbert-Space Formulation of Quantum Mechanics
• Scattering theory using smeared non-Hermitian potentials
• Perturbed Defects and T-Systems in Conformal Field Theory
• Fluctuations and skewness of the current in the partially asymmetric exclusion process
• Quantum Phase Transition in a Pseudo-hermitian Dicke model
• Exact Isospectral Pairs of PT-Symmetric Hamiltonians
• Asymptotically vanishing PT-symmetric potentials and negative-mass Schroedinger equations
• Identification of observables in quantum toboggans
• Conjecture on the analyticity of PT-symmetric potentials and the reality of their spectra
• Cryptohermitian Picture of Scattering Using Quasilocal Metric Operators
• On the ODE/IM correspondence for minimal models
• Complex WKB Analysis of a PT Symmetric Eigenvalue Problem
• Geometry of PT-symmetric quantum mechanics
• Faster than Hermitian Time Evolution
• PT-symmetry and Integrability