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 10
Kramers-Kronig relations 1

How this entity was disambiguated

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 ⓘ
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

Referenced by (11)

Full triples — surface form annotated when it differs from this entity's canonical label.

Hendrik Anthony Kramers → notableWork → Kramers–Kronig relations ⓘ
Hendrik Anthony Kramers → knownFor → Kramers–Kronig relations ⓘ
Hendrik Anthony Kramers → hasEponym → Kramers–Kronig relations ⓘ
Kubo formula → involves → Kramers-Kronig relations ⓘ
linked to: Kramers–Kronig relations
Cauchy principal value → usedIn → Kramers–Kronig relations ⓘ
Hendrik Anthony Kramers → knownFor → Kramers–Kronig relations ⓘ
subject linked to: Kramers
Kramers → hasEponymousConcept → Kramers–Kronig relations ⓘ
Kramers–Heisenberg dispersion formula → usesConcept → Kramers–Kronig relations ⓘ
Kramers–Heisenberg dispersion formula → relatedTo → Kramers–Kronig relations ⓘ
Hilbert transform → usedFor → Kramers–Kronig relations ⓘ
Hilbert transform → relatedConcept → Kramers–Kronig relations ⓘ