{\mathcal {PT}}-symmetric models in curved manifolds

DOI10.1088/1751-8113/43/48/485204zbMath1207.81030arXiv1001.2988OpenAlexW3125214050MaRDI QIDQ3066008

Petr Siegl, David Krejčiřík

Publication date: 7 January 2011

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

Full work available at URL: https://arxiv.org/abs/1001.2988

Mathematics Subject Classification ID

Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) (34L40) Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Completeness of eigenfunctions and eigenfunction expansions in context of PDEs (35P10) Nonselfadjoint operator theory in quantum theory including creation and destruction operators (81Q12) Quantum mechanics on special spaces: manifolds, fractals, graphs, lattices (81Q35)

Related Items (14)

On local perturbations of waveguides ⋮ Pseudospectra in non-Hermitian quantum mechanics ⋮ Spectra of definite type in waveguide models ⋮ On the similarity of Sturm-Liouville operators with non-Hermitian boundary conditions to self-adjoint and normal operators ⋮ Guiding structures with multiply connected cross sections: Evolution of propagation in external fields at complex Robin parameters ⋮ Perfect transmission scattering as a \(\mathcal{PT}\)-symmetric spectral problem ⋮ \({\mathcal{PT}}\)-symmetric Laplace-Beltrami operator in the strip on a sphere ⋮ Contact interactions and Kronig–Penney models in Hermitian and $ \boldsymbol {\mathcal {PT}}$ symmetric quantum mechanics ⋮ \({\mathcal{PT}}\)-symmetric square well-perturbations and the existence of metric operator ⋮ Resonant alteration of propagation in guiding structures with complex Robin parameter and its magnetic-field-induced restoration ⋮ Complex symmetric completions of partial operator matrices ⋮ Non-self-adjoint graphs ⋮ Hidden symmetries in non-self-adjoint graphs ⋮ The collapse of quasi-self-adjointness at the exceptional points of a PT -symmetric model with complex Robin boundary conditions

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