Localization of exceptional points with Padé approximants
Résumé
The strict coalescence of two resonance states may never happen (due to the sensitivity to small external perturbations). However its existence can have noticeable effects on measurable quantities. The coalescence of resonances is associated with Exceptional Points (EPs) in the spectrum of the system under study. The determination of exceptional points is often a hard numerical task, due to the need to calculate many eigenvalues of a non-Hermitian Hamiltonian as function of the potential's parameters which are to be varied adiabatically. The method presented here is based on the Padé algorithm. This enables one to calculate the EPs with a small number of solutions. As an illustrative numerical example an EP of H + 2 in strong laser fields is calculated.
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