Abstract We consider the general response theory recently proposed by Ruelle for describing the impact of small perturbations to the non-equilibrium steady states resulting from Axiom A dynamical systems. We show that the causality of the response functions entails the possibility of writing a set of Kramers-Kronig relations for the corresponding susceptibilities at all orders of nonlinearity. ...

We review dispersion relations, which relate the real part of the optical susceptibility (refraction) to the imaginary part (absorption). We derive and discuss these relations as applied to nonlinear optical systems. It is shown that in the nonlinear case, for self-action effects the correct form for such dispersion relations is nondegenerate, i.e. it is necessary to use multiple frequency argu...

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...

In order to deduce the experimental beam conditions from the observed x-ray line emission spectrum of high Z elements, atomic radiative data for transition energies and oscillator strengths, ion-atom impact ionization cross sections, Coster-Kronig yields, and fluorescence yield are needed. In this paper, we report on calculations to study the dependence of these atomic data on ionization stage....

Relativistic calculations of nonradiative transition rates to K, L, and M -shell vacancy statesin Ni-, Cu-, and Zn-like ions with Z=32, 36, 42, 47, 56, 60, 66, 74, 83, and 92 are performed.Auger and Coster-Kronig transition probabilities are calculated using both Dirac-Hartree-Fockand model-potential wave functions. Tabulated data are presented for Kand L-shells Augerrates in Ni...

Because direct measurements of the refractive index of hemoglobin over a large wavelength range are challenging, indirect methods deserve particular attention. Among them, the Kramers-Kronig relations are a powerful tool often used to derive the real part of a refractive index from its imaginary part. However, previous attempts to apply the relations to solutions of human hemoglobin have been s...

The modulational instability, a destabilization mechanism for plane waves, occurs ubiquitously in spatially extended dynamical systems arising in fluid dynamics, nonlinear optics, atomic physics, and other disciplines. In this paper, we investigate analytically, numerically, and experimentally the modulational instability in a layered cubically nonlinear (Kerr) optical medium that consists of a...

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...

The bounded one dimensional multibarrier potential shows signs of chaos, phase transition and a transmission probability of unity for certain values of its total length L and the ratio c of total interval to total width. Like the infinite Kronig-Penney system, which is arranged along the whole spatial region, the bounded multibarrier potential has a band-gap structure in its energy spectrum. Bu...