Bender-Wu singularities

DOI10.1063/1.4972290zbMath1353.81052arXiv1607.00190OpenAlexW2468192979MaRDI QIDQ2951750

Vincenzo Grecchi, Riccardo Giachetti

Publication date: 9 January 2017

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

Full work available at URL: https://arxiv.org/abs/1607.00190

Mathematics Subject Classification ID

Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) (34L40) General spectral theory of ordinary differential operators (34L05) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10)

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Cites Work

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• Analytic continuation of eigenvalues of a quartic oscillator
• Localization of the states of a \(PT\)-symmetric double well
• Nodal properties of the scaled quartic anharmonic oscillator
• Perturbation theory of odd anharmonic oscillators
• Unfolding the quartic oscillator
• On the reality of the eigenvalues for a class of \(\mathcal{PT}\)-symmetric oscillators
• A class of analytic perturbations for one-body Schrödinger Hamiltonians
• Spectral analysis of the complex cubic oscillator
• Numerical evidence that the perturbation expansion for a non-Hermitian PT-symmetric Hamiltonian is Stieltjes
• Level crossings in aPT-symmetric double well
• The top resonances of the cubic oscillator
• PT-symmetric operators and metastable states of the 1D relativistic oscillators
• Bender-Wu branch points in the cubic oscillator
• Equivalence of unstable anharmonic oscillators and double wells
• 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
• Exact quantization condition for anharmonic oscillators (in one dimension)
• Singular perturbation of polynomial potentials in the complex domain with applications to PT-symmetric families
• The semiclassical small-ℏ limit of loci of roots of subdominant solutions for polynomial potentials