Closed form expressions for the Green’s function of a quantum graph—a scattering approach

DOI10.1088/1751-8121/ad03a5arXiv2309.11251MaRDI QIDQ6086632

Gregor Tanner, Unnamed Author, Sven Gnutzmann

Publication date: 10 November 2023

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

Full work available at URL: https://arxiv.org/abs/2309.11251

zbMATH Keywords

Green's functionsquantum graphswave scattering

Mathematics Subject Classification ID

Estimates of eigenvalues in context of PDEs (35P15) Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Water waves, gravity waves; dispersion and scattering, nonlinear interaction (76B15) Wave equation (35L05) Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.) (05C70) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) (S)-matrix theory, etc. in quantum theory (81U20) Distance in graphs (05C12) Decomposition theory for (C^*)-algebras (46L45) Green's functions for elliptic equations (35J08) Quantum dots, waveguides, ratchets, etc. (81Q37)

Cites Work

• Unnamed Item
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• Green's function approach for quantum graphs: an overview
• The trace formula for quantum graphs with general self adjoint boundary conditions
• Topological resonances on quantum graphs
• Elastodynamics on graphs—wave propagation on networks of plates
• Sturm-Liouville eigenvalue problems on networks
• Kirchhoff's rule for quantum wires
• Green function approach for general quantum graphs
• Note on the Applicability of the Free-Electron Network Model to Metals

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