Multiple Exceptional Points in APT–Symmetric Cantor Multilayers

Rational Points in Cantor Sets

The Idea for this article was given by a problem in real analysis. We wanted to determine the one-dimensional Lebesgue-measure of the set f(C)9 where C stands for the classical triadic Cantor set and/is the Cantor-function, which is also known as "devil's staircase." We could see immediately that to determine the above measure we needed to know which dyadic rationals were contained in C. We soo...

Exceptional points in atomic spectra.

We report the existence of exceptional points for the hydrogen atom in crossed magnetic and electric fields in numerical calculations. The resonances of the system are investigated and it is shown how exceptional points can be found by exploiting characteristic properties of the degeneracies, which are branch point singularities. A possibility for the observation of exceptional points in an exp...

Non-differentiability points of Cantor functions

Fano profiles in scattering around exceptional points

In a previous paper it has been shown that the interference of the first and second order pole of the Green’s function at an exceptional point, as well as the interference of the first order poles in the vicinity of the exceptional point, gives rise to asymmetric scattering cross section profiles. In the present paper we demonstrate that these line profiles are indeed well described by the Beut...

Exceptional points in bichromatic Wannier–Stark systems

The resonance spectrum of a tilted periodic quantum system for a bichromatic periodic potential is investigated. For such a bichromatic Wannier–Stark system, exceptional points, degeneracies of the spectrum, can be localized in parameter space by means of an efficient method for computing resonances. Berry phases and Petermann factors are analysed. Finally, the influence of a nonlinearity of th...