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 | 3 |
| 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
ⓘ
surface form:
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 operator formulation of quantum mechanics
ⓘ
surface form:
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
ⓘ
surface form:
Kramers-Kronig relations
causality conditions ⓘ time integrals of correlation functions ⓘ |
| isPartOf |
fluctuation–dissipation theorem
ⓘ
surface form:
Green-Kubo relations
|
| 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
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Instruction
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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 (4)
Full triples — surface form annotated when it differs from this entity's canonical label.
this entity surface form:
Kubo formula for transport coefficients