Pseudo-orbit approach to trajectories of resonances in quantum graphs with general vertex coupling: Fermi rule and high-energy asymptotics

DOI10.1063/1.4979048zbMath1360.81169arXiv1608.03978OpenAlexW2513592534MaRDI QIDQ2981024

Jiří Lipovský, Pavel Exner

Publication date: 8 May 2017

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

Full work available at URL: https://arxiv.org/abs/1608.03978

Mathematics Subject Classification ID

Spectrum, resolvent (47A10) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Asymptotic properties of solutions to ordinary differential equations (34D05) Series expansions (e.g., Taylor, Lidstone series, but not Fourier series) (41A58) Quantum mechanics on special spaces: manifolds, fractals, graphs, lattices (81Q35) Resonance phenomena for ordinary differential equations involving randomness (34F15)

Related Items (2)

Unnamed Item ⋮ On the multilevel internal structure of the asymptotic distribution of resonances

Cites Work

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• Resonance asymptotics in the generalized Winter model
• Non-Weyl resonance asymptotics for quantum graphs
• A general approximation of quantum graph vertex couplings by scaled Schrödinger operators on thin branched manifolds
• A Fermi golden rule for quantum graphs
• On the effective size of a non-Weyl graph
• Finite pseudo orbit expansions for spectral quantities of quantum graphs
• Non-Weyl asymptotics for quantum graphs with general coupling conditions
• Resonances from perturbations of quantum graphs with rationally related edges

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