Exceptional points in the spectra of atoms in external fields

Abstract

We investigate exceptional points, which are branch point singularities of two resonance eigenstates, in spectra of the hydrogen atom in crossed external electric and magnetic fields. A procedure to systematically search for exceptional points is presented, and their existence is proven. The properties of the branch point singularities are discussed with effective low-dimensional matrix models, their relation with avoided level crossings is analyzed, and their influence on dipole matrix elements and the photoionization cross section is investigated. Furthermore, the rare case of a connection between three resonances almost forming a triple-degeneracy in the form of a cubic root branch point is discussed.

12 pages, 9 figures, 1 table

References in corpus (6)

• Visualization of Branch Points in PT-Symmetric Waveguides
• A non-Hermitian $PT-$symmetric Bose-Hubbard model: eigenvalue rings from unfolding higher-order exceptional points
• Exceptional Points in Atomic Spectra
• Coupling of eigenvalues of complex matrices at diabolic and exceptional points
• Coulomb analogy for nonhermitian degeneracies near quantum phase transitions
• Resonance solutions of the nonlinear Schrödinger equation in an open double-well potential