Eigenvalue dynamics of a \(\mathcal{PT}\)-symmetric Sturm-Liouville operator and criteria for similarity to a self-adjoint or a normal operator
DOI10.1134/S1064562417060230zbMath1385.81021arXiv1707.08210OpenAlexW2963270198MaRDI QIDQ1707158
A. A. Shkalikov, S. N. Tumanov
Publication date: 28 March 2018
Published in: Doklady Mathematics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1707.08210
Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) (34L40) Sturm-Liouville theory (34B24) Hermitian and normal operators (spectral measures, functional calculus, etc.) (47B15) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Exactly and quasi-solvable systems arising in quantum theory (81U15) Finite-dimensional groups and algebras motivated by physics and their representations (81R05) Bessel and Airy functions, cylinder functions, ({}_0F_1) (33C10)
Cites Work
- Unnamed Item
- The limit spectral graph in semiclassical approximation for the Sturm-Liouville problem with complex polynomial potential
- Spectral portraits of the Orr-Sommerfeld operator with large Reynolds numbers
- A Krein space approach to \(PT\) symmetry
- The limit behavior of the spectrum for large parameter values in a model problem
- Point interactions: \(\mathcal{PT}\)-Hermiticity and reality of the spectrum.
- Supersymmetry and the spontaneous breakdown of 𝒫𝒯 symmetry
- On the eigenproblems of PT-symmetric oscillators
- Perturbations of self-adjoint and normal operators with discrete spectrum
- 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
- Singular perturbation of polynomial potentials in the complex domain with applications to PT-symmetric families
- Eigenvalues of -symmetric oscillators with polynomial potentials
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