Kramers–Kronig relations
E415080
The Kramers–Kronig relations are fundamental mathematical formulas in physics that connect the real and imaginary parts of a complex response function, expressing how causality constrains the frequency-dependent behavior of physical systems.
All labels observed (2)
| Label | Occurrences |
|---|---|
| Kramers–Kronig relations canonical | 8 |
| Kramers-Kronig relations | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T4141999 — 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: Kramers–Kronig relations Context triple: [Hendrik Anthony Kramers, notableWork, Kramers–Kronig relations]
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A.
Onsager reciprocal relations
Onsager reciprocal relations are fundamental symmetry relations in nonequilibrium thermodynamics that link pairs of coupled fluxes and forces, showing that certain transport coefficients are equal.
-
B.
Esaki–Tsu relation
The Esaki–Tsu relation is a fundamental formula in semiconductor physics that describes the nonlinear current–voltage characteristics and negative differential conductivity of electrons in superlattices under high electric fields.
-
C.
Wiener–Khinchin theorem
The Wiener–Khinchin theorem is a fundamental result in signal processing and probability theory that relates a wide-sense stationary random process’s autocorrelation function to its power spectral density via the Fourier transform.
-
D.
Bhabha–Corben equations
The Bhabha–Corben equations are relativistic wave equations in quantum electrodynamics that describe the dynamics of spinning charged particles, developed by physicists Homi J. Bhabha and H. C. Corben.
-
E.
Lifshitz–Kosevich formula
The Lifshitz–Kosevich formula is a key theoretical expression in solid-state physics that describes how the amplitude of quantum oscillations in metals depends on temperature, magnetic field, and electronic properties.
- 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: Kramers–Kronig relations Target entity description: The Kramers–Kronig relations are fundamental mathematical formulas in physics that connect the real and imaginary parts of a complex response function, expressing how causality constrains the frequency-dependent behavior of physical systems.
-
A.
Onsager reciprocal relations
Onsager reciprocal relations are fundamental symmetry relations in nonequilibrium thermodynamics that link pairs of coupled fluxes and forces, showing that certain transport coefficients are equal.
-
B.
Esaki–Tsu relation
The Esaki–Tsu relation is a fundamental formula in semiconductor physics that describes the nonlinear current–voltage characteristics and negative differential conductivity of electrons in superlattices under high electric fields.
-
C.
Wiener–Khinchin theorem
The Wiener–Khinchin theorem is a fundamental result in signal processing and probability theory that relates a wide-sense stationary random process’s autocorrelation function to its power spectral density via the Fourier transform.
-
D.
Bhabha–Corben equations
The Bhabha–Corben equations are relativistic wave equations in quantum electrodynamics that describe the dynamics of spinning charged particles, developed by physicists Homi J. Bhabha and H. C. Corben.
-
E.
Lifshitz–Kosevich formula
The Lifshitz–Kosevich formula is a key theoretical expression in solid-state physics that describes how the amplitude of quantum oscillations in metals depends on temperature, magnetic field, and electronic properties.
- F. None of above. chosen
Statements (48)
| Predicate | Object |
|---|---|
| instanceOf |
causality relation in physics
ⓘ
dispersion relation ⓘ mathematical relation ⓘ |
| appliesTo |
causal Green’s functions
ⓘ
dielectric function ⓘ frequency-dependent susceptibilities ⓘ impedance functions ⓘ linear response functions ⓘ optical conductivity ⓘ refractive index ⓘ scattering amplitudes ⓘ susceptibility in linear response theory ⓘ |
| assumes | sufficiently fast decay of response at high frequency ⓘ |
| basedOn |
Cauchy integral formula
ⓘ
Hilbert transform ⓘ analyticity of complex functions ⓘ causality ⓘ |
| category | complex analysis in physics ⓘ |
| domain | frequency domain ⓘ |
| expresses | connection between dispersion and dissipation ⓘ |
| field |
condensed matter physics
ⓘ
electrical engineering ⓘ mathematical physics ⓘ optics ⓘ signal processing ⓘ theoretical physics ⓘ |
| hasConsequence | sum rules for response functions ⓘ |
| hasForm | integral transform ⓘ |
| implies |
dispersion is constrained by absorption
ⓘ
real and imaginary parts of a causal response are not independent ⓘ |
| mathematicalNature | pair of coupled integral equations ⓘ |
| namedAfter |
Hendrik Anthony Kramers
ⓘ
Ralph Kronig ⓘ |
| relatedTo |
fluctuation–dissipation theorem
ⓘ
surface form:
Fluctuation–dissipation theorem
Hilbert transform ⓘ analytic continuation ⓘ |
| relates |
imaginary part of a response function
ⓘ
real part of a response function ⓘ |
| requires |
causal time-domain response
ⓘ
system linearity ⓘ time invariance ⓘ |
| usedFor |
checking consistency of experimental optical data
ⓘ
data inversion in spectroscopy ⓘ deriving dispersion from absorption measurements ⓘ reconstructing phase from amplitude spectra ⓘ validating linear response models ⓘ |
| uses | principal value integral ⓘ |
| yearProposed | 1926 ⓘ |
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: Kramers–Kronig relations Description of subject: The Kramers–Kronig relations are fundamental mathematical formulas in physics that connect the real and imaginary parts of a complex response function, expressing how causality constrains the frequency-dependent behavior of physical systems.
Referenced by (9)
Full triples — surface form annotated when it differs from this entity's canonical label.
this entity surface form:
Kramers-Kronig relations