Mathematical and Physical Meaning of the Crossings of Energy Levels in $${\mathscr {PT}}$$ PT -Symmetric Systems

DOI10.1007/978-3-319-31356-6_13zbMath1402.81149arXiv1303.4876OpenAlexW3099380590MaRDI QIDQ4555429

Miloslav Znojil, Denis I. Borisov

Publication date: 20 November 2018

Published in: Springer Proceedings in Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1303.4876

zbMATH Keywords

phase transitionreal spectrumquantum phase transitionexceptional pointdynamical regime

Mathematics Subject Classification ID

Hilbert and pre-Hilbert spaces: geometry and topology (including spaces with semidefinite inner product) (46C05) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Nonselfadjoint operator theory in quantum theory including creation and destruction operators (81Q12)

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Cites Work

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• \(\mathcal P\mathcal T\)-symmetric harmonic oscillators
• Smeared quantum lattices exhibiting 𝒫𝒯-symmetry with positive 𝒫
• Non-Selfadjoint Operators in Quantum Physics
• PSEUDO-HERMITIAN REPRESENTATION OF QUANTUM MECHANICS
• Horizons of stability