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...

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...

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...

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...

The development of different forms of measurement models for impedance has allowed examination of key assumptions on which the use of such models to assess error structure are based. The stochastic error structures obtained using the transfer-function and Voigt measurement models were identical, even when non-stationary phenomena caused some of the data to be inconsistent with the Kramers–Kroni...

Unstable atomic nuclei release excess energy through various radioactive decay processes. In some cases, including internal conversion and electron capture, the atom remains ionised after the nuclear decay event. Atomic relaxation back to the ground state occurs rapidly via radiative and non-radiative processes, often referred to collectively as atomic radiations. Non-radiative processes includ...

Lβ2 X-ray satellite spectra of tungsten and gold are calculated using the Multi-Configuration Dirac-Fock energies and compared with recent experimental data. New calculations of L1-L3M5 Coster-Kronig transition energies for tungsten are presented, confirming the origin of the Lβ2 visible satellites reported by two experimental groups. We found the value 5.09 eV for the average energy of the L1-...

We report the observation of laser gain in the vacuum ultraviolet pumped by super Coster-Kronig decay. Using a 5-J, 300-psec pump pulse of 1064-nm radiation, we have observed gain on transitions in Zn III at 127.0, 130.6, and 131.9 nm with total gains of exp(2.4), exp(5.1), and exp(3.2), respectively. The large branching ratios of the rapid super Coster-Kronig decay into a small number of final...

The Kronig-Penney model is typically used to compute the band structure and bound states of a periodic crystal. While the model allows analytical solutions, it does so by simplifying the potential to a periodic square potential. We present a method of using transfer matrices to compute energy bands in a 1-Dimensional lattice. This method does not involve the simplification required by the Kroni...