Migdal approximation
E59621
approximation in electron-phonon theory
approximation in many-body physics
theoretical approximation
The Migdal approximation is a theoretical simplification in many-body physics that neglects vertex corrections in electron-phonon interactions, justified when phonon energies are much smaller than electronic energies.
All labels observed (3)
| Label | Occurrences |
|---|---|
| Migdal theorem | 2 |
| Migdal approximation canonical | 1 |
| Migdal–Watson approximation | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T478150 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Migdal approximation Context triple: [Eliashberg theory, assumes, Migdal approximation]
-
A.
Herzberg–Teller approximation
The Herzberg–Teller approximation is a refinement in molecular spectroscopy that accounts for vibronic coupling by allowing electronic transition dipole moments to depend on nuclear coordinates, explaining intensity in otherwise forbidden transitions.
-
B.
Born–Huang expansion
The Born–Huang expansion is a quantum mechanical method that systematically improves upon the Born–Oppenheimer approximation by including couplings between electronic and nuclear motions in molecular systems.
-
C.
Feynman checkerboard model
The Feynman checkerboard model is a path-integral-based lattice model introduced by Richard Feynman to illustrate and derive the behavior of relativistic quantum particles, particularly the Dirac equation in one spatial dimension.
-
D.
Born–Oppenheimer approximation
The Born–Oppenheimer approximation is a fundamental method in molecular quantum mechanics that simplifies calculations by treating nuclear motion as much slower than electronic motion, allowing their behaviors to be separated.
-
E.
Rayleigh–Schrödinger perturbation theory
Rayleigh–Schrödinger perturbation theory is a fundamental method in quantum mechanics for approximating the energies and states of a system by treating interactions as small corrections to an exactly solvable problem.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Migdal approximation Target entity description: The Migdal approximation is a theoretical simplification in many-body physics that neglects vertex corrections in electron-phonon interactions, justified when phonon energies are much smaller than electronic energies.
-
A.
Herzberg–Teller approximation
The Herzberg–Teller approximation is a refinement in molecular spectroscopy that accounts for vibronic coupling by allowing electronic transition dipole moments to depend on nuclear coordinates, explaining intensity in otherwise forbidden transitions.
-
B.
Born–Huang expansion
The Born–Huang expansion is a quantum mechanical method that systematically improves upon the Born–Oppenheimer approximation by including couplings between electronic and nuclear motions in molecular systems.
-
C.
Feynman checkerboard model
The Feynman checkerboard model is a path-integral-based lattice model introduced by Richard Feynman to illustrate and derive the behavior of relativistic quantum particles, particularly the Dirac equation in one spatial dimension.
-
D.
Born–Oppenheimer approximation
The Born–Oppenheimer approximation is a fundamental method in molecular quantum mechanics that simplifies calculations by treating nuclear motion as much slower than electronic motion, allowing their behaviors to be separated.
-
E.
Rayleigh–Schrödinger perturbation theory
Rayleigh–Schrödinger perturbation theory is a fundamental method in quantum mechanics for approximating the energies and states of a system by treating interactions as small corrections to an exactly solvable problem.
- F. None of above. chosen
Statements (44)
| Predicate | Object |
|---|---|
| instanceOf |
approximation in electron-phonon theory
ⓘ
approximation in many-body physics ⓘ theoretical approximation ⓘ |
| appliesTo | electron-phonon interactions ⓘ |
| assumes |
electrons respond much faster than lattice vibrations
ⓘ
phonon energies are much smaller than electronic energies ⓘ small ratio of phonon frequency to Fermi energy ⓘ |
| basedOn | separation of energy scales between electrons and phonons ⓘ |
| contrastsWith | approaches including full vertex corrections ⓘ |
| field |
condensed matter physics
ⓘ
many-body physics ⓘ |
| formalism |
Feynman diagram expansion
ⓘ
many-body Green's function theory ⓘ |
| goal | make electron-phonon problems analytically and numerically tractable ⓘ |
| historicallyAttributedTo | Arkady Migdal ⓘ |
| implies |
electron-phonon coupling can be treated perturbatively
ⓘ
vertex corrections are of higher order in small mass ratio ⓘ |
| justifiedWhen |
Migdal parameter is small
ⓘ
ion mass is much larger than electron mass ⓘ |
| mayBreakDownWhen |
electron-phonon coupling is very strong
ⓘ
phonon energies become comparable to electronic energies ⓘ systems are non-adiabatic ⓘ |
| neglects |
higher-order electron-phonon scattering processes involving vertex corrections
ⓘ
vertex corrections in electron-phonon interaction diagrams ⓘ |
| relatedConcept |
Migdal-Eliashberg theory
ⓘ
linked to:
Eliashberg theory
adiabatic limit ⓘ electron-phonon self-energy ⓘ mass renormalization parameter lambda ⓘ |
| relatedTo |
Migdal theorem
ⓘ
linked to:
Migdal approximation
|
| simplifies |
diagrammatic treatment of electron-phonon interactions
ⓘ
self-consistent calculations in Eliashberg theory ⓘ |
| timePeriod | mid-20th century ⓘ |
| usedFor |
computing superconducting transition temperatures in conventional superconductors
ⓘ
describing electron lifetime due to electron-phonon scattering ⓘ describing quasiparticle mass renormalization by phonons ⓘ |
| usedIn |
Eliashberg theory
ⓘ
calculations of electron self-energy due to phonons ⓘ calculations of phonon-induced renormalization of electronic bands ⓘ first-principles calculations of electron-phonon coupling in metals ⓘ theory of conventional superconductivity ⓘ theory of phonon-mediated pairing in superconductors ⓘ |
| uses | lowest-order electron-phonon self-energy diagrams ⓘ |
| validityDependsOn |
adiabatic approximation
ⓘ
smallness of characteristic phonon frequency compared to Fermi energy ⓘ |
How these facts were elicited
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Instruction
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Input
Subject: Migdal approximation Description of subject: The Migdal approximation is a theoretical simplification in many-body physics that neglects vertex corrections in electron-phonon interactions, justified when phonon energies are much smaller than electronic energies.
Referenced by (4)
Full triples — surface form annotated when it differs from this entity's canonical label.
linked to: Migdal approximation
linked to: Migdal approximation
linked to: Migdal approximation