Approximations by graphs and emergence of global structures

DOI10.1016/S0034-4877(06)80031-5zbMath1142.81007arXivquant-ph/0508226MaRDI QIDQ2480644

Pavel Hejčík, Pavel Exner, Petr Šeba

Publication date: 3 April 2008

Published in: Reports on Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/quant-ph/0508226

zbMATH Keywords

approximationSchrödinger equationSinai billiardtransport propertieslattice quantum graphs

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Applications of operator theory in the physical sciences (47N50) Transport processes in time-dependent statistical mechanics (82C70) Linear difference operators (47B39)

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Cites Work

• Unnamed Item
• Free quantum motion on a branching graph
• A discrete nodal domain theorem for trees
• Graph Laplacians, nodal domains, and hyperplane arrangements
• Resonance statistics in a microwave cavity with a thin antenna
• Star graphs and \v Seba billiards
• Scattering on graphs and one-dimensional approximations to N-dimensional Schrödinger operators
• A single-mode quantum transport in serial-structure geometric scatterers
• Quantum motion on a half-line connected to a plane
• Kirchhoff's rule for quantum wires
• A duality between Schroedinger operators on graphs and certain Jacobi matrices
• Quantum graphs: a simple model for chaotic scattering
• Scattering on compact manifolds with infinitely thin horns
• Graph models for waves in thin structures

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