Intrinsic exceptional point -- a challenge in quantum theory

• URL: http://arxiv.org/abs/2411.12501v1
• Date: Tue, 19 Nov 2024 13:40:30 GMT
• Title: Intrinsic exceptional point -- a challenge in quantum theory
• Authors: Miloslav Znojil,
• Abstract summary: In spite of its unbroken $cal PT-$symmetry, the popular imaginary cubic oscillator Hamiltonian $H(IC)=p2+rm ix3$ does not satisfy all of the necessary postulates of quantum mechanics. The failure is due to the intrinsic exceptional point'' (IEP) features of $H(IC)$ and, in particular, to the phenomenon of a high-energy parallelization of its bound-state-mimicking eigenvectors.
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• Abstract: In spite of its unbroken ${\cal PT}-$symmetry, the popular imaginary cubic oscillator Hamiltonian $H^{(IC)}=p^2+{\rm i}x^3$ does not satisfy all of the necessary postulates of quantum mechanics. The failure is due to the ``intrinsic exceptional point'' (IEP) features of $H^{(IC)}$ and, in particular, to the phenomenon of a high-energy asymptotic parallelization of its bound-state-mimicking eigenvectors. In the paper it is argued that the operator $H^{(IC)}$ (and the like) can only be interpreted as a manifestly unphysical, singular IEP limit of a hypothetical one-parametric family of certain standard quantum Hamiltonians. For explanation, an ample use is made of perturbation theory and of multiple analogies between IEPs and conventional Kato's exceptional points.

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