\(\mathcal{RT}\)-symmetric Laplace operators on star graphs: real spectrum and self-adjointness

DOI10.1155/2015/649795zbMath1337.81062OpenAlexW1743149844WikidataQ59102528 ScholiaQ59102528MaRDI QIDQ277932

Muhammad Usman, Pavel Kurasov, Maria Astudillo

Publication date: 2 May 2016

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

Full work available at URL: https://doi.org/10.1155/2015/649795

Mathematics Subject Classification ID

Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Finite-dimensional groups and algebras motivated by physics and their representations (81R05) Quantum mechanics on special spaces: manifolds, fractals, graphs, lattices (81Q35)

Related Items (8)

Kagome network with vertex coupling of a preferred orientation ⋮ PT-symmetric quantum graphs ⋮ Quantum graphs: PT-symmetry and reflection symmetry of the spectrum ⋮ Self-adjoint restrictions of maximal operator on graph ⋮ Complex Magnetic Fields: An Improved Hardy--Laptev--Weidl Inequality and Quasi-Self-Adjointness ⋮ Quantum graphs: self-adjoint, and yet exhibiting a nontrivial \(\mathcal{PT}\)-symmetry ⋮ The Schrödinger equation on a star-shaped graph under general coupling conditions ⋮ Hidden symmetries in non-self-adjoint graphs

Cites Work

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• Spectra ofPT-symmetric operators and perturbation theory
• 𝓟𝓣-symmetric quantum mechanics
• Quadratic ${\mathcal P}{\mathcal T}$-symmetric operators with real spectrum and similarity to self-adjoint operators
• Non-self-adjoint graphs
• symmetric non-self-adjoint operators, diagonalizable and non-diagonalizable, with a real discrete spectrum

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