Third-order spectral branch points in Krein space related setups: $$\mathcal{P}\mathcal{T}$$ -symmetric matrix toy model, MHD α 2-dynamo and extended Squire equation

DOI10.1007/s10582-005-0113-zzbMath1465.81025arXivmath-ph/0506021OpenAlexW3125326655WikidataQ61954494 ScholiaQ61954494MaRDI QIDQ5000484

Frank Stefani, Uwe Günther

Publication date: 14 July 2021

Published in: Czechoslovak Journal of Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math-ph/0506021

zbMATH Keywords

Krein spacelevel crossingsbranch pointsnon-Hermitian operatorsdiscrete symmetriesJordan structureSquire equationMHD dynamo

Mathematics Subject Classification ID

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

Related Items

Quasi-exact minus-quartic oscillators in strong-core regime, Projective Hilbert space structures at exceptional points, Fixing D7-brane positions by F-theory fluxes

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Pseudo-supersymmetric quantum mechanics and isospectral pseudo-Hermitian Hamiltonians
• A Krein space approach to \(PT\) symmetry
• Analytic perturbation theory for matrices and operators. Licensed ed
• Quasi-Hermitian operators in quantum mechanics and the variational principle
• Complex Extension of Quantum Mechanics
• MHD α2-dynamo, Squire equation and PT-symmetric interpolation between square well and harmonic oscillator
• Experimental demonstration of a homogeneous two-scale dynamo
• Quantal phase factors accompanying adiabatic changes
• Diabolical points in the spectra of triangles
• Computation of multiple eigenvalues and generalized eigenvectors for matrices dependent on parameters
• Avoided level crossings and Riemann sheet structure
• Unfolding a diabolic point: a generalized crossing scenario
• 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
• Space of state vectors in 𝒫𝒯-symmetric quantum mechanics
• Pseudo-Hermiticity versus PT symmetry: The necessary condition for the reality of the spectrum of a non-Hermitian Hamiltonian
• Isospectrality of spherical MHD dynamo operators: Pseudo-hermiticity and a no-go theorem