Exceptional points in atomic resonance spectra

Holger Cartarius

Universität Stuttgart, 1. Institut für Theoretische Physik, Stuttgart, Germany

Exceptional points can appear in parameter-dependent open quantum systems, at which both the complex energy eigenvalues and the wave functions describing two or even more resonances of the system pass through a branch point singularity as functions of the parameters, i.e., become identical. The existence of resonances, i.e., decaying unbound states, is important for the appearance of exceptional points because the coalescence of discrete eigenstates with identical eigenvectors is not possible in the spectra of Hermitian Hamiltonians with potentials, which describe bound states. A real physical system which is accessible theoretically and experimentally and which exhibits exceptional points is the hydrogen atom in crossed static electric and magnetic fields. It is shown how exceptional points can be detected in numerical calculations and how they can be described with low-dimensional matrix models. Important phenomena such as the unique time-behaviour of decaying resonances at an exceptional point are demonstrated and the rare case of a connection between three resonances almost forming a triple-degeneracy in the form of a cubic root branch point is presented.

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