High- and low-frequency asymptotic consequences of the Kramers-Kronig relations
ثبت نشده
چکیده
This paper examines the highand low-frequency asymptotic consequences of the Kramers-Kronig relations which hold for the real and imaginary parts of the Fourier transform of the response of any linear causal system. By knowing or assuming the highor low-frequency expansion of one of these functions, the corresponding asymptotic expansion of the other is easily determined, and furthermore the coefficients in this expansion may be determined by evaluating integrals that involve intermediate frequencies. The practical utility of the approach is demonstrated with examples from floating-body hydrodynamics and some new integral relations are derived and exploited.
منابع مشابه
Optical properties of silicon nano layers by using Kramers- Kronig method
Silicon thin layers are deposited on glass substrates with the thickness of 103 nm, 147 nm and 197 nm. The layers are produced with electron gun evaporation method under ultra-high vacuum condition. The optical Reectance and the Transmittance of produced layers were measured by using spectrophotometer. The optical functions such as, real and imaginary part of refractive index, real and imaginar...
متن کاملApplication of Measurement Models to Impedance Spectroscopy III. Evaluation of Consistency with the Kramers-Kronig Relations
The Kramers-Kronig equations and the current methods used to apply them to electrochemical impedance spectra are reviewed. Measurement models are introduced as 'a tool for identification of the frequency-dependent error structure of impedance data and for evaluating the consistency of the data with the Kramers-Kronig relations. Through the use of a measurement model, experimental data can be ch...
متن کاملWhat did Kramers and Kronig do and how did they do it?
Over time the account of how the Kramers–Kronig (dispersion) relations between the real and imaginary parts of response functions were derived in 1926 and 1927 has been transmogrified into anecdotes about what might have been done but was not. Although Kramers obtained both members of a pair of relations, Kronig obtained only one. Both authors appealed to specific models of an atomic gas rather...
متن کاملKramers-Kronig Relations and the Properties of Conductivity and Permittivity in Heterogeneous Media
The macroscopic electric permittivity of a given medium may depend on frequency, but this frequency dependence cannot be arbitrary, its real and imaginary parts are related by the well-known Kramers-Kronig relations. Here, we show that an analogous paradigm applies to the macroscopic electric conductivity. If the causality principle is taken into account, there exists Kramers-Kronig relations f...
متن کاملCausality, Kramers-Kronig Relations, and Landau Damping
We review the consequence of the causality in electrodynamics. The Kramers-Kronig relations are direct consequence of causality which has two ingredients: no perturbation in the remote past and irrelevance of future susceptibility to the present field. It is shown that the dielectric function obtained from the integration along the Landau contour can be derived from the Kramers-Kronig relations...
متن کامل