We extend the standard Kronig-Penney model with periodic δ potentials to the cases with generalized contact interactions under the assumption that the system has time-reversal symmetry. By applying Bloch theorem, the eigenvalue equation which determines the dispersion relation for onedimensional periodic array of the generalized contact interactions is deduced within the framework of the transf...

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...

We consider a complex periodic PT-symmetric potential of the Kronig-Penney type, in order to elucidate the peculiar properties found by Bender et al. for potentials of the form V = i(sin x)2N+1, and in particular the absence of anti-periodic solutions. In this model we show explicitly why these solutions disappear as soon as V (x) 6= V (x), and spell out the consequences for the form of the dis...

We propose a model for realizing frequency-dependent spatial variations of the probe susceptibility in cold atomic sample. It is found that usual Kramers-Kronig (KK) relation between real and imaginary parts frequency domain can be mapped into space as far detuned control field intensity linearly varied used. This non-Hermitian medium exhibits then unidirectional reflectionless band photons inc...

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...