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arXiv · 2010.15014

Non-Hermitian N-state degeneracies: unitary realizations via antisymmetric anharmonicities

Miloslav Znojil
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Abstract

The phenomenon of degeneracy of an $N-$plet of bound states is studied in the framework of quantum theory of closed (i.e., unitary) systems. For an underlying Hamiltonian $H=H(\lambda)$ the degeneracy occurs at a Kato's exceptional point $\lambda^{(EPN)}$ of order $N$ and of the spectral geometric multiplicity $K 2$ and $K>1$ benchmark models of the process of degeneracy becomes feasible and non-numerical for a broad class of specific, maximally non-Hermitian anharmonic-oscillator toy-model Hamiltonians. An exhaustive classification of non-equivalent processes is given by a partitioning of the unperturbed spectrum into equidistant and centered unperturbed subspectra.

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Miloslav Znojil. 2020-10-28. Non-Hermitian N-state degeneracies: unitary realizations via antisymmetric anharmonicities. https://arxiv.org/abs/2010.15014

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