Sharp diameter bound on the spectral gap for quantum graphs

DOI10.1090/proc/15090zbMath1465.81038arXiv1905.03071OpenAlexW3159222387MaRDI QIDQ4990344

Livia Corsi, David Borthwick, Kenny Jones

Publication date: 28 May 2021

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1905.03071

Mathematics Subject Classification ID

Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) (34L40) General spectral theory of ordinary differential operators (34L05) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Boundary value problems on graphs and networks for ordinary differential equations (34B45) Quantum mechanics on special spaces: manifolds, fractals, graphs, lattices (81Q35)

Related Items (4)

Impediments to diffusion in quantum graphs: Geometry-based upper bounds on the spectral gap ⋮ Sturm-Liouville problems and global bounds by small control sets and applications to quantum graphs ⋮ On the hot spots of quantum graphs ⋮ Upper eigenvalue bounds for the Kirchhoff Laplacian on embedded metric graphs

Cites Work

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• On the spectral gap of a quantum graph
• Rayleigh estimates for differential operators on graphs
• Quantum graphs which optimize the spectral gap
• Extremal properties of eigenvalues for a metric graph.
• Surgery principles for the spectral analysis of quantum graphs
• Spectral gap for quantum graphs and their edge connectivity
• Edge connectivity and the spectral gap of combinatorial and quantum graphs
• Dependence of the spectrum of a quantum graph on vertex conditions and edge lengths

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