Spectral asymptotics of the Laplacian on Platonic solids graphs

DOI10.1063/1.5116100zbMath1431.81063arXiv1906.09091OpenAlexW2952946520WikidataQ126538305 ScholiaQ126538305MaRDI QIDQ5218760

Pavel Exner, Jiří Lipovský

Publication date: 5 March 2020

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

Full work available at URL: https://arxiv.org/abs/1906.09091

Mathematics Subject Classification ID

Polyhedra and polytopes; regular figures, division of spaces (51M20) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Quantum mechanics on special spaces: manifolds, fractals, graphs, lattices (81Q35)

Related Items (6)

Kagome network with vertex coupling of a preferred orientation ⋮ Spectrum of periodic chain graphs with time-reversal non-invariant vertex coupling ⋮ Magnetic square lattice with vertex coupling of a preferred orientation ⋮ Topological bulk-edge effects in quantum graph transport ⋮ Quantum graphs: self-adjoint, and yet exhibiting a nontrivial \(\mathcal{PT}\)-symmetry ⋮ Magnetic ring chains with vertex coupling of a preferred orientation

Cites Work

• Convergence of spectra of graph-like thin manifolds
• Quantum graphs with vertices of a preferred orientation
• Non-Weyl asymptotics for quantum graphs with general coupling conditions
• Eigenvalue Estimates for the Weighted Laplacian on Metric Trees
• Schrödinger operators on graphs and geometry. III. General vertex conditions and counterexamples
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