Projective Hilbert space structures at exceptional points

DOI10.1088/1751-8113/40/30/014zbMath1120.81035arXiv0704.1291OpenAlexW3104669498MaRDI QIDQ5757556

Boris F. Samsonov, Uwe Günther, Ingrid Rotter

Publication date: 7 September 2007

Published in: Journal of Physics A: Mathematical and Theoretical (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0704.1291

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Applications of functional analysis in quantum physics (46N50) Differential geometric methods, including holonomy, Berry and Hannay phases, Aharonov-Bohm effect, etc. in quantum theory (81Q70) Operator algebra methods applied to problems in quantum theory (81R15)

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Cites Work

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• Dynamical systems VIII. Singularity theory. II: Classification and applications. Transl. from the Russian by J. S. Joel
• A return to observability near exceptional points in a schematic \(\mathcal P\mathcal T\)-symmetric model
• Analytic perturbation theory for matrices and operators. Licensed ed
• On singular features of acoustic wave propagation in weakly dissipative anisotropic thermoviscoelasticity
• Topics in cohomological studies of algebraic varieties. Impanga lecture notes
• Numerical linear algebra and solvability of partial differential equations
• Dynamics of quantum systems embedded in a continuum
• Supersymmetry and the spontaneous breakdown of 𝒫𝒯 symmetry
• Complex Extension of Quantum Mechanics
• Faster than Hermitian Quantum Mechanics
• THE SOLUTION OF SOME PERTURBATION PROBLEMS FOR MATRICES AND SELFADJOINT OR NON-SELFADJOINT DIFFERENTIAL EQUATIONS I
• MHD α2-dynamo, Squire equation and PT-symmetric interpolation between square well and harmonic oscillator
• Quantal phase factors accompanying adiabatic changes
• Gamow-Jordan vectors and non-reducible density operators from higher-order S-matrix poles
• Berry phase of a resonant state
• Unfolding a diabolic point: a generalized crossing scenario
• Coupling of eigenvalues of complex matrices at diabolic and exceptional points
• SUSY transformations between diagonalizable and non-diagonalizable Hamiltonians
• Nonlinear superposition formulas based on imprimitive group action
• Pseudo-Hermiticity for a class of nondiagonalizable Hamiltonians
• 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
• The optical singularities of bianisotropic crystals
• Non-Hermitian quantum mechanics of non-diagonalizable Hamiltonians: puzzles with self-orthogonal states