The theory of optical properties of nanoparticles is considered with the aid of dispersion relations, which are based on the Kramers-Kronig analysis. It is shown that one can utilize rather general dispersion relations, which hold for liquid matrices that contain nanoparticles. Wiener bounds incorporating the Kramers-Kronig analysis are utilized in assessment of the complex permittivity of a na...

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...

Subdiffusion in the presence of an external force field can be described in phase space by the fractional Klein-Kramers equation. In this paper, we explore the stochastic structure of this equation. Using a subordination method, we define a random process whose probability density function is a solution of the fractional Klein-Kramers equation. The structure of the introduced process agrees wit...

A treatise on the optical property of biological tissue is presented. Water is postulated to be a topological basis and serves to discriminate published skin data. Electromagnetic theory governing dielectric behavior is concisely detailed pertaining to certain optical constants and Kramers-Krönig relation. The Kramers-Krönig relation defining dispersion index is emulated through the discrete Hi...

Our current understanding of the absorption and emission properties of interstellar grains are reviewed. The constraints placed by the Kramers-Kronig relation on the wavelength-dependence and the maximum allowable quantity of the dust absorption are discussed. Comparisons of the opacities (mass absorption coefficients) derived from interstellar dust models with those directly estimated from obs...

transmittance and reflectance, the imaginary part can be determined from transmittance data alone. It is possible to use Kramers-Kronig analysis to calculate the real part if the imaginary part is known over a sufficiently broad range. We show that the delta calculated from reflection and transmission data without taking into account roughness may underestimate the real part of the refractive i...

The diffusion of adatoms and molecules on a surface at low coverage can be measured by helium scattering. The experimental observable is the dynamic structure factor. In this article, we show how Kramers’ turnover theory can be used to infer physical properties of the diffusing particle from the experiment. Previously, Chudley and Elliot showed, under reasonable assumptions, that the dynamic st...

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...