An existence criterion for the \(\mathcal{PT}\)-symmetric phase transition

DOI10.3934/DCDSB.2014.19.1955zbMath1312.34129OpenAlexW2323222546MaRDI QIDQ478685

Sandro Graffi, Emanuela Caliceti

Publication date: 4 December 2014

Published in: Discrete and Continuous Dynamical Systems. Series B (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/dcdsb.2014.19.1955

zbMATH Keywords

phase transition\(\mathcal{PT}\)-symmetry

Mathematics Subject Classification ID

Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) (34L40) Eigenvalues, estimation of eigenvalues, upper and lower bounds of ordinary differential operators (34L15)

Related Items (4)

A pseudo-Hermitian \(\beta\)-Hermite family of matrices ⋮ Diverging Eigenvalues in Domain Truncations of Schrödinger Operators with Complex Potentials ⋮ Non-real eigenvalues for \(\mathcal{PT}\)-symmetric double wells ⋮ PT-symmetry and Schrödinger operators. The double well case

Cites Work

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• Spectral equivalences, Bethe ansatz equations, and reality properties in 𝒫𝒯-symmetric quantum mechanics
• Supersymmetry and the spontaneous breakdown of 𝒫𝒯 symmetry
• Must a Hamiltonian be Hermitian?
• {\cal PT} symmetry breaking and exceptional points for a class of inhomogeneous complex potentials
• Generalized PT symmetry and real spectra
• Real Spectra in Non-Hermitian Hamiltonians Having<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi mathvariant="bold-script">P</mml:mi><mml:mi mathvariant="bold-script">T</mml:mi></mml:math>Symmetry
• 𝓟𝓣-symmetric quantum mechanics

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