On Agmon metrics and exponential localization for quantum graphs

DOI10.1007/s00220-018-3124-xzbMath1388.81130arXiv1508.06922OpenAlexW2962785308WikidataQ115608992 ScholiaQ115608992MaRDI QIDQ1749348

Evans M. II. Harrell, Anna V. Maltsev

Publication date: 16 May 2018

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

Full work available at URL: https://arxiv.org/abs/1508.06922

Mathematics Subject Classification ID

Eigenfunctions, eigenfunction expansions, completeness of eigenfunctions of ordinary differential operators (34L10) Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory (81Q20) Distance in graphs (05C12) Quantum mechanics on special spaces: manifolds, fractals, graphs, lattices (81Q35)

Related Items (8)

Magnetic Schrödinger operators and landscape functions ⋮ Sturm-Liouville problems and global bounds by small control sets and applications to quantum graphs ⋮ On the hot spots of quantum graphs ⋮ Regularized potentials of Schrödinger operators and a local landscape function ⋮ Elliptic differential operators on infinite graphs with general conditions on vertices ⋮ Localization and landscape functions on quantum graphs ⋮ Localization for Anderson models on metric and discrete tree graphs ⋮ Fast localization of eigenfunctions via smoothed potentials

Cites Work

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• Poisson eigenvalue statistics for random Schrödinger operators on regular graphs
• Introduction to spectral theory. With applications to Schrödinger operators
• Anderson localization for radial tree-like random quantum graphs
• Kirchhoff's rule for quantum wires
• Eigenvalue Estimates for the Weighted Laplacian on Metric Trees
• Quantum graphs: I. Some basic structures
• On the spectrum of the Laplacian on regular metric trees

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