Graph-like models for thin waveguides with Robin boundary conditions

DOI10.3233/ASY-2010-1014zbMath1227.35238arXiv0803.4314OpenAlexW1544318368MaRDI QIDQ3082148

Claudio Cacciapuoti, Domenico Finco

Publication date: 9 March 2011

Published in: Asymptotic Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0803.4314

zbMATH Keywords

quantum graphsconstrained dynamicsasymptotic dynamics of quantum systems

Mathematics Subject Classification ID

Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Perturbation theories for operators and differential equations in quantum theory (81Q15) PDEs on graphs and networks (ramified or polygonal spaces) (35R02)

Related Items (12)

Competing nonlinearities in NLS equations as source of threshold phenomena on star graphs ⋮ Quantum Information Measures of the One‐Dimensional Robin Quantum Well ⋮ Quantum graphs: Coulomb-type potentials and exactly solvable models ⋮ 1D Schrödinger operators with short range interactions: two-scale regularization of distributional potentials ⋮ Singularity of eigenfunctions at the junction of shrinking tubes. I ⋮ Peaked and Low Action Solutions of NLS Equations on Graphs with Terminal Edges ⋮ Singularity of eigenfunctions at the junction of shrinking tubes. Part II ⋮ Diffusion processes in thin tubes and their limits on graphs ⋮ One-dimensional Schrödinger operators with singular potentials: a Schwartz distributional formulation ⋮ Scale invariant effective Hamiltonians for a graph with a small compact core ⋮ Planar waveguide with “twisted” boundary conditions: Small width ⋮ Thin waveguides with Robin boundary conditions

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