Peierls substitution
E136242
Peierls substitution is a quantum mechanical method for incorporating the effects of an external electromagnetic field into the momentum of charged particles in lattice or solid-state systems.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Peierls substitution canonical | 2 |
How this entity was disambiguated
This entity first appeared as the object of triple T1190366 — 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: Peierls substitution Context triple: [Rudolf Peierls, notableIdea, Peierls substitution]
-
A.
Pippard nonlocal theory
Pippard nonlocal theory is a refinement of superconductivity theory that introduces spatially nonlocal relations between current and electromagnetic fields to account for finite coherence length effects beyond the London model.
-
B.
Eliashberg theory
Eliashberg theory is an extension of BCS superconductivity that incorporates strong-coupling and frequency-dependent effects to more accurately describe real superconducting materials.
-
C.
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.
-
D.
London equations
The London equations are fundamental relations in superconductivity that describe how magnetic fields behave inside superconductors, capturing key features like the Meissner effect and zero electrical resistance.
-
E.
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.
- 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: Peierls substitution Target entity description: Peierls substitution is a quantum mechanical method for incorporating the effects of an external electromagnetic field into the momentum of charged particles in lattice or solid-state systems.
-
A.
Pippard nonlocal theory
Pippard nonlocal theory is a refinement of superconductivity theory that introduces spatially nonlocal relations between current and electromagnetic fields to account for finite coherence length effects beyond the London model.
-
B.
Eliashberg theory
Eliashberg theory is an extension of BCS superconductivity that incorporates strong-coupling and frequency-dependent effects to more accurately describe real superconducting materials.
-
C.
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.
-
D.
London equations
The London equations are fundamental relations in superconductivity that describe how magnetic fields behave inside superconductors, capturing key features like the Meissner effect and zero electrical resistance.
-
E.
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.
- F. None of above. chosen
Statements (47)
| Predicate | Object |
|---|---|
| instanceOf |
quantum mechanical method
ⓘ
solid-state physics technique ⓘ theoretical physics concept ⓘ |
| actsOn |
crystal momentum of electrons
ⓘ
hopping terms in tight-binding Hamiltonians ⓘ |
| appliesTo |
electrons in solids
ⓘ
lattice systems ⓘ tight-binding models ⓘ |
| approximationType |
effective low-energy description
ⓘ
semi-classical approximation ⓘ |
| assumes | slowly varying electromagnetic fields on lattice scale ⓘ |
| basedOn | minimal coupling prescription ⓘ |
| captures |
effect of magnetic field via Peierls phase
ⓘ
orbital coupling of electrons to magnetic field ⓘ |
| category |
electromagnetic coupling method in lattices
ⓘ
quantum lattice modeling technique ⓘ |
| domain |
lattice gauge theory (effective, non-fundamental use)
ⓘ
theoretical modeling ⓘ |
| effect |
encodes magnetic flux through lattice plaquettes
ⓘ
introduces complex phase factors in hopping amplitudes ⓘ |
| field |
condensed matter physics
ⓘ
quantum mechanics ⓘ solid-state physics ⓘ |
| formalism |
replaces hopping t by t·exp(i phase from vector potential)
ⓘ
replaces momentum operator p by p − qA in lattice context ⓘ |
| historicalContext | introduced in early development of solid-state quantum theory ⓘ |
| limitations |
approximate for strong-field, short-wavelength regimes
ⓘ
less accurate for rapidly varying fields ⓘ |
| namedAfter | Rudolf Peierls ⓘ |
| purpose |
incorporate external electromagnetic field effects
ⓘ
modify particle momentum in a lattice ⓘ |
| relatedTo |
Aharonov–Bohm effect in lattices
ⓘ
linked to:
Aharonov–Bohm effect
gauge invariance ⓘ minimal coupling in continuum ⓘ vector potential of electromagnetic field ⓘ |
| usedFor |
describing electron dynamics in magnetic fields
ⓘ
introducing gauge fields in lattice Hamiltonians ⓘ modeling charged particles in periodic potentials ⓘ studying Bloch electrons in magnetic fields ⓘ studying Hofstadter butterfly spectrum ⓘ studying quantum Hall effects in lattice models ⓘ |
| usedIn |
modeling graphene in magnetic fields
ⓘ
modeling superconducting vortex lattices (effective lattice models) ⓘ modeling topological insulators on lattices ⓘ numerical simulations of lattice electrons in fields ⓘ |
| validIn |
non-relativistic quantum mechanics
ⓘ
tight-binding approximation ⓘ |
How these facts were elicited
The pipeline generated the facts above by prompting gpt-5.1 with this entity's name + description and the instruction below.
Instruction
You are a knowledge base construction expert. Given a subject entity and a description of it, return factual statements that you know for the subject as a JSON list of dictionaries(triples), where keys must be "subject", "predicate" and "object". The number of facts may be very high, between 25 to 50 or more, for very popular subjects. For less popular subjects, the number of facts can be very low, like 5 or 10. # Requirements - If you don't know the subject at all, return an empty list. - If the subject is not a named entity, return an empty list. - Include at least one triple where predicate is "instanceOf". - Do not get too wordy. - Separate several objects into multiple triples with one object.
Input
Subject: Peierls substitution Description of subject: Peierls substitution is a quantum mechanical method for incorporating the effects of an external electromagnetic field into the momentum of charged particles in lattice or solid-state systems.
Referenced by (2)
Full triples — surface form annotated when it differs from this entity's canonical label.
subject linked to:
Peierls