Topological resonances on quantum graphs

DOI10.1007/s00023-018-0672-8zbMath1388.81128arXiv1604.01732OpenAlexW2963716272WikidataQ130096057 ScholiaQ130096057MaRDI QIDQ1750633

Françoise Truc, Yves Colin de Verdière

Publication date: 22 May 2018

Published in: Annales Henri Poincaré (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1604.01732

Mathematics Subject Classification ID

Quantum chaos (81Q50) (2)-body potential quantum scattering theory (81U05) Distance in graphs (05C12) Resonance in context of PDEs (35B34) Quantum mechanics on special spaces: manifolds, fractals, graphs, lattices (81Q35)

Related Items (9)

Scattering resonances of large weakly open quantum graphs ⋮ Closed form expressions for the Green’s function of a quantum graph—a scattering approach ⋮ Non-compact quantum graphs with summable matrix potentials ⋮ Standing waves for the NLS on the double-bridge graph and a rational-irrational dichotomy ⋮ Eigenspaces of symmetric graphs are not typically irreducible ⋮ On Pleijel's nodal domain theorem for quantum graphs ⋮ On the multilevel internal structure of the asymptotic distribution of resonances ⋮ Spectrum of a non-selfadjoint quantum star graph ⋮ Knots and signal transmission in topological quantum devices

Cites Work

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• A Fermi golden rule for quantum graphs
• Relationship between scattering matrix and spectrum of quantum graphs
• Resonances from perturbations of quantum graphs with rationally related edges
• Quantum graphs: a simple model for chaotic scattering
• On the level spacing distribution in quantum graphs.

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