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

• URL: http://arxiv.org/abs/2010.15014v1
• Date: Wed, 28 Oct 2020 14:41:52 GMT
• Title: Non-Hermitian N-state degeneracies: unitary realizations via antisymmetric anharmonicities
• Authors: Miloslav Znojil
• Abstract summary: 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.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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 $K<N$. In spite of the phenomenological appeal of the concept (tractable as a quantum phase transition, or as a unitary processes of the loss of the observability of the system), the dedicated literature deals, predominantly, just with the models where $N=2$ and $K=1$. In our paper it is shown that the construction of the $N>2$ 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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