The spectrum of magnetic Schrödinger operators on a graph with periodic structure.

DOI10.1006/jfan.1999.3478zbMath1073.47517OpenAlexW2082054977MaRDI QIDQ1969451

Yusuke Higuchi, Tomoyuki Shirai

Publication date: 1999

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jfan.1999.3478

zbMATH Keywords

phase transitiondiscrete magnetic Laplaciandiscrete spectral geometryabelian covering graphtwisted operator

Mathematics Subject Classification ID

Applications of PDEs on manifolds (58J90) Linear difference operators (47B39)

Related Items (14)

Magnetic Energies and Feynman–Kac–Itô Formulas for Symmetric Markov Processes ⋮ Spectra of Schrödinger operators on equilateral quantum graphs ⋮ Invariants for Laplacians on periodic graphs ⋮ The spectrum of non-local discrete Schrödinger operators with a \(\delta\)-potential ⋮ Schrödinger operators with guided potentials on periodic graphs ⋮ Trace formulas for magnetic Schrödinger operators on periodic graphs and their applications ⋮ Dirac and magnetic Schrödinger operators on fractals ⋮ Weak Bloch property for discrete magnetic Schrödinger operators ⋮ Scattering on periodic metric graphs ⋮ Magnetic Schrödinger operators on periodic discrete graphs ⋮ Laplacians on periodic graphs with guides ⋮ Schrödinger operators with potential waveguides on periodic graphs ⋮ Trace formulas for Schrödinger operators on periodic graphs ⋮ A local test for global extrema in the dispersion relation of a periodic graph

Cites Work

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• Kazhdan groups acting on compact manifolds
• Gauss polynomials and the rotation algebra
• Asymptotic behavior of the transition probability of a random walk on an infinite graph
• Connection of the dual space of a group with the structure of its closed subgroups
• Periodic Schrödinger Operators on a Manifold
• Discrete Schrödinger operators on a graph
• Single Band Motion of Conduction Electrons in a Uniform Magnetic Field

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