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.

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All labels observed (3)

Label	Occurrences
Migdal theorem	2
Migdal approximation canonical	1
Migdal–Watson approximation	1

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	Eliashberg theory ⓘ surface form: Migdal-Eliashberg theory adiabatic limit ⓘ electron-phonon self-energy ⓘ mass renormalization parameter lambda ⓘ
relatedTo	Migdal approximation self-linksurface differs ⓘ surface form: Migdal theorem
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 ⓘ

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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.

Eliashberg theory → assumes → Migdal approximation ⓘ

Migdal approximation → relatedTo → Migdal approximation self-linksurface differs ⓘ

this entity surface form: Migdal theorem

Arkady Migdal → notableWork → Migdal approximation ⓘ

this entity surface form: Migdal–Watson approximation

Arkady Migdal → notableWork → Migdal approximation ⓘ

this entity surface form: Migdal theorem