Kubo formula
E166674
The Kubo formula is a fundamental result in linear response theory that expresses transport coefficients and response functions in terms of equilibrium correlation functions in statistical mechanics and quantum many-body physics.
All labels observed (2)
| Label | Occurrences |
|---|---|
| Kubo formula canonical | 4 |
| Kubo formula for transport coefficients | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T1462444 — 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: Kubo formula Context triple: [fluctuation–dissipation theorem, isSpecialCaseOf, Kubo formula]
-
A.
Feynman–Kac formula
The Feynman–Kac formula is a fundamental result connecting solutions of certain partial differential equations with expectations over stochastic processes, forming a bridge between quantum mechanics, probability theory, and mathematical finance.
-
B.
Euler–Maclaurin summation formula
The Euler–Maclaurin summation formula is a fundamental result in analysis that connects sums and integrals, providing powerful asymptotic expansions and error estimates for approximating series by integrals.
-
C.
Riemann–Siegel formula
The Riemann–Siegel formula is an asymptotic expression that efficiently approximates the Riemann zeta function on the critical line, playing a key role in the numerical study of its zeros.
-
D.
Itô’s lemma
Itô’s lemma is a fundamental result in stochastic calculus that generalizes the chain rule to functions of stochastic processes, especially Brownian motion.
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E.
Wick’s theorem
Wick’s theorem is a fundamental result in quantum field theory that expresses time-ordered products of field operators as sums of normal-ordered products with all possible contractions, forming the basis for deriving Feynman rules and diagrammatic expansions.
- 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: Kubo formula Target entity description: The Kubo formula is a fundamental result in linear response theory that expresses transport coefficients and response functions in terms of equilibrium correlation functions in statistical mechanics and quantum many-body physics.
-
A.
Feynman–Kac formula
The Feynman–Kac formula is a fundamental result connecting solutions of certain partial differential equations with expectations over stochastic processes, forming a bridge between quantum mechanics, probability theory, and mathematical finance.
-
B.
Euler–Maclaurin summation formula
The Euler–Maclaurin summation formula is a fundamental result in analysis that connects sums and integrals, providing powerful asymptotic expansions and error estimates for approximating series by integrals.
-
C.
Riemann–Siegel formula
The Riemann–Siegel formula is an asymptotic expression that efficiently approximates the Riemann zeta function on the critical line, playing a key role in the numerical study of its zeros.
-
D.
Itô’s lemma
Itô’s lemma is a fundamental result in stochastic calculus that generalizes the chain rule to functions of stochastic processes, especially Brownian motion.
-
E.
Wick’s theorem
Wick’s theorem is a fundamental result in quantum field theory that expresses time-ordered products of field operators as sums of normal-ordered products with all possible contractions, forming the basis for deriving Feynman rules and diagrammatic expansions.
- F. None of above. chosen
Statements (49)
| Predicate | Object |
|---|---|
| instanceOf |
physical law
ⓘ
result in linear response theory ⓘ theoretical physics concept ⓘ |
| appliesTo |
dielectric response
ⓘ
electrical conductivity ⓘ magnetic susceptibility ⓘ spin conductivity ⓘ thermal conductivity ⓘ viscosity ⓘ |
| assumes |
initial thermal equilibrium
ⓘ
linear regime of response ⓘ small external perturbations ⓘ |
| basedOn |
fluctuation-dissipation theorem
ⓘ
linked to:
fluctuation–dissipation theorem
|
| category |
response theory
ⓘ
transport theory ⓘ |
| describes | linear response of a system to external perturbations ⓘ |
| field |
condensed matter physics
ⓘ
linear response theory ⓘ nonequilibrium statistical mechanics ⓘ quantum many-body physics ⓘ statistical mechanics ⓘ |
| formulatedIn | Heisenberg picture ⓘ |
| gives |
dc transport coefficients in zero-frequency limit
ⓘ
frequency-dependent response functions ⓘ |
| hasMathematicalForm | response function equals integral of commutator of observables with perturbation operator ⓘ |
| historicalPublicationPeriod | 1950s ⓘ |
| influenced | modern condensed matter theory ⓘ |
| involves |
Kramers-Kronig relations
ⓘ
linked to:
Kramers–Kronig relations
causality conditions ⓘ time integrals of correlation functions ⓘ |
| isPartOf |
Green-Kubo relations
ⓘ
linked to:
fluctuation–dissipation theorem
|
| namedAfter | Ryogo Kubo ⓘ |
| relates |
response functions to equilibrium correlation functions
ⓘ
transport coefficients to equilibrium correlation functions ⓘ |
| usedIn |
Hall conductivity calculations
ⓘ
Kubo-Greenwood formula for conductivity ⓘ anomalous Hall effect theory ⓘ derivation of Fourier law of heat conduction ⓘ derivation of Navier-Stokes transport coefficients ⓘ derivation of Ohm law from microscopic theory ⓘ diagrammatic techniques in condensed matter physics ⓘ linear optical response calculations ⓘ many-body perturbation theory ⓘ quantum transport theory ⓘ |
| uses |
current-current correlation functions
ⓘ
equilibrium ensemble averages ⓘ retarded Green functions ⓘ stress tensor correlation functions ⓘ time-correlation functions ⓘ |
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: Kubo formula Description of subject: The Kubo formula is a fundamental result in linear response theory that expresses transport coefficients and response functions in terms of equilibrium correlation functions in statistical mechanics and quantum many-body physics.
Referenced by (5)
Full triples — surface form annotated when it differs from this entity's canonical label.
linked to: Kubo formula