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 |
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
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Instruction
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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