A return to observability near exceptional points in a schematic \(\mathcal P\mathcal T\)-symmetric model

DOI10.1016/J.PHYSLETB.2007.01.046zbMath1248.81050arXivquant-ph/0701232OpenAlexW2040642879MaRDI QIDQ712983

Miloslav Znojil

Publication date: 18 October 2012

Published in: Physics Letters. B (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/quant-ph/0701232

zbMATH Keywords

\(\mathcal P\mathcal T\)-symmetric quantum models

Mathematics Subject Classification ID

Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10)

Related Items (9)

Anomalous mechanisms of the loss of observability in non-Hermitian quantum models ⋮ Classification of the conditionally observable spectra exhibiting central symmetry ⋮ Solvable model of quantum phase transitions and the symbolic-manipulation-based study of its multiply degenerate exceptional points and of their unfolding ⋮ The Coulomb potential and the paradoxes of PT symmetrization ⋮ \({\mathcal{PT}}\)-symmetric periodic optical potentials ⋮ Conditional observability ⋮ Projective Hilbert space structures at exceptional points ⋮ Smeared quantum lattices exhibiting 𝒫𝒯-symmetry with positive 𝒫 ⋮ Exceptional points and domains of unitarity for a class of strongly non-Hermitian real-matrix Hamiltonians

Cites Work

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• A positive-definite scalar product for free Proca particle
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• Quasi-Hermitian operators in quantum mechanics and the variational principle
• On the reality of the eigenvalues for a class of \(\mathcal{PT}\)-symmetric oscillators
• Equivalence of unstable anharmonic oscillators and double wells
• Systematic search for 𝒫𝒯-symmetric potentials with real energy spectra
• Closed formula for the metric in the Hilbert space of a -symmetric model

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