Recovering quantum graphs from their Bloch spectrum

DOI10.5802/aif.2786zbMath1301.35195arXiv1101.6002OpenAlexW2963475982MaRDI QIDQ381162

Ralf Rueckriemen

Publication date: 15 November 2013

Published in: Annales de l'Institut Fourier (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1101.6002

zbMATH Keywords

inverse spectral problemquantum graphBloch spectrum

Mathematics Subject Classification ID

Inverse problems for PDEs (35R30) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Isospectrality (58J53) PDEs on graphs and networks (ramified or polygonal spaces) (35R02)

Related Items (3)

Anomalous nodal count and singularities in the dispersion relation of honeycomb graphs ⋮ Stability of eigenvalues of quantum graphs with respect to magnetic perturbation and the nodal count of the eigenfunctions ⋮ A geometric construction of isospectral magnetic graphs

Cites Work

• First order approach and index theorems for discrete and metric graphs
• Inverse spectral results on even dimensional tori
• Periodic orbit theory and spectral statistics for quantum graphs
• Jacobian tori associated with a finite graph and its abelian covering graphs
• Can one hear the shape of a graph?
• Inverse Spectral Results on Two-Dimensional Tori
• Quantum graphs: an introduction and a brief survey
• The isospectral fruits of representation theory: quantum graphs and drums
• On isospectral periodic potentials in Rn. II
• Can One Hear the Shape of a Drum?
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