Approximations of quantum-graph vertex couplings by singularly scaled rank-one operators

DOI10.1007/s11005-014-0706-1zbMath1300.81045arXiv1310.5856OpenAlexW2032695545MaRDI QIDQ464335

Pavel Exner, Stepan S. Manko

Publication date: 17 October 2014

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

Full work available at URL: https://arxiv.org/abs/1310.5856

zbMATH Keywords

approximationquantum graphvertex coupling

Mathematics Subject Classification ID

Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) (S)-matrix theory, etc. in quantum theory (81U20) Quantum mechanics on special spaces: manifolds, fractals, graphs, lattices (81Q35)

Related Items (7)

Two-parametric ${\delta'}$ -interactions: approximation by Schrödinger operators with localized rank-two perturbations ⋮ Scattering of flexural waves in Euler–Bernoulli beams by short-range potentials ⋮ Kreı̆n Formula and Convergence of Hamiltonians with Scaled Potentials in Dimension One ⋮ Schrödinger operators with singular rank-two perturbations and point interactions ⋮ Dirac-Krein systems on star graphs ⋮ Scale invariant effective Hamiltonians for a graph with a small compact core ⋮ Families of one-point interactions resulting from the squeezing limit of the sum of two- and three-delta-like potentials

Cites Work

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• Some remarks on the \(\delta\) '-interaction in one dimension
• Weakly coupled states on branching graphs
• A general approximation of quantum graph vertex couplings by scaled Schrödinger operators on thin branched manifolds
• Approximations of quantum-graph vertex couplings by singularly scaled potentials
• Contact interactions on graph superlattices
• Kirchhoff's rule for quantum wires
• Green function approach for general quantum graphs

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