ODE/IM correspondence, the Glossary
In mathematical physics, the ODE/IM correspondence is a link between ordinary differential equations (ODEs) and integrable models.[1]
Table of Contents
9 relations: Bethe ansatz, Integrable system, Magnetism, Mathematical physics, Ordinary differential equation, Quantum Heisenberg model, Schrödinger equation, Spectral theory, WKB approximation.
- Integrable systems
- Spin models
Bethe ansatz
In physics, the Bethe ansatz is an ansatz for finding the exact wavefunctions of certain quantum many-body models, most commonly for one-dimensional lattice models.
See ODE/IM correspondence and Bethe ansatz
Integrable system
In mathematics, integrability is a property of certain dynamical systems. ODE/IM correspondence and Integrable system are Integrable systems.
See ODE/IM correspondence and Integrable system
Magnetism
Magnetism is the class of physical attributes that occur through a magnetic field, which allows objects to attract or repel each other.
See ODE/IM correspondence and Magnetism
Mathematical physics
Mathematical physics refers to the development of mathematical methods for application to problems in physics.
See ODE/IM correspondence and Mathematical physics
Ordinary differential equation
In mathematics, an ordinary differential equation (ODE) is a differential equation (DE) dependent on only a single independent variable. ODE/IM correspondence and ordinary differential equation are ordinary differential equations.
See ODE/IM correspondence and Ordinary differential equation
Quantum Heisenberg model
The quantum Heisenberg model, developed by Werner Heisenberg, is a statistical mechanical model used in the study of critical points and phase transitions of magnetic systems, in which the spins of the magnetic systems are treated quantum mechanically. ODE/IM correspondence and quantum Heisenberg model are spin models.
See ODE/IM correspondence and Quantum Heisenberg model
Schrödinger equation
The Schrödinger equation is a partial differential equation that governs the wave function of a quantum-mechanical system.
See ODE/IM correspondence and Schrödinger equation
Spectral theory
In mathematics, spectral theory is an inclusive term for theories extending the eigenvector and eigenvalue theory of a single square matrix to a much broader theory of the structure of operators in a variety of mathematical spaces.
See ODE/IM correspondence and Spectral theory
WKB approximation
In mathematical physics, the WKB approximation or WKB method is a method for finding approximate solutions to linear differential equations with spatially varying coefficients.
See ODE/IM correspondence and WKB approximation
See also
Integrable systems
- AKNS system
- Bäcklund transform
- Benjamin–Ono equation
- Bullough–Dodd model
- Calogero–Degasperis–Fokas equation
- Camassa–Holm equation
- DBAR problem
- Davey–Stewartson equation
- Dispersionless equation
- Drinfeld–Sokolov–Wilson equation
- Dym equation
- Ernst equation
- Four-dimensional Chern–Simons theory
- Frobenius manifold
- Gardner equation
- Gelfand–Zeitlin integrable system
- Hitchin system
- Integrable algorithm
- Integrable system
- Inverse scattering transform
- Ishimori equation
- Kadomtsev–Petviashvili equation
- Kaup–Kupershmidt equation
- Korteweg–De Vries equation
- Liouville–Arnold theorem
- List of integrable models
- Modified Korteweg-De Vries equation
- Nahm equations
- Nonlinear Schrödinger equation
- Novikov–Veselov equation
- ODE/IM correspondence
- Riemann–Hilbert problem
- Six-dimensional holomorphic Chern–Simons theory
- Soliton
- Superintegrable Hamiltonian system
- Tau function (integrable systems)
- Toda field theory
- Toda lattice
- Volterra lattice
- W-algebra
- Ward's conjecture
Spin models
- AKLT model
- ANNNI model
- Boolean network
- Chiral Potts model
- Classical Heisenberg model
- Gaudin model
- Glauber dynamics
- Haldane–Shastry model
- Ising model
- J1 J2 model
- Majumdar–Ghosh model
- ODE/IM correspondence
- Potts model
- Quantum Heisenberg model
- Quantum rotor model
- Spin chain
- Spin model
- Sznajd model
- Transverse-field Ising model
- Two-dimensional critical Ising model
- ZN model