Generic asymptotics of resonance counting function for Schrödinger point interactions

DOI10.1007/978-3-030-31531-3_8zbMath1453.35057arXiv1803.06039OpenAlexW2790591905MaRDI QIDQ5118011

Illya M. Karabash, Sergio A. Albeverio

Publication date: 26 August 2020

Published in: Analysis as a Tool in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1803.06039

zbMATH Keywords

multigraphdirected graphexponential polynomialWeyl-type asymptoticsdelta-interactionasymptotics of resonancesquasi-normal-eigenvalue

Mathematics Subject Classification ID

Applications of graph theory (05C90) Asymptotic distributions of eigenvalues in context of PDEs (35P20) Schrödinger operator, Schrödinger equation (35J10) Resonance in context of PDEs (35B34) Special quantum systems, such as solvable systems (81Q80) Quantum dots, waveguides, ratchets, etc. (81Q37)

Related Items (2)

On real resonances for three-dimensional Schrödinger operators with point interactions ⋮ Asymptotics of Random Resonances Generated by a Point Process of Delta-Interactions

Cites Work

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• Spectral analysis on graph-like spaces
• On the critical exponent in an isoperimetric inequality for chords
• Polynomial bound on the number of scattering poles
• The resonance counting function for Schrödinger operators with generic potentials
• Sharp polynomial bounds on the number of scattering poles
• Perturbation of resonances in quantum mechanics
• Open quantum systems and Feynman integrals
• Scattering problems on noncompact graphs
• Optimization of quasi-normal eigenvalues for Krein-Nudelman strings
• Non-Weyl resonance asymptotics for quantum graphs
• Pareto optimal structures producing resonances of minimal decay under \(L^1\)-type constraints
• Von Neumann-Wigner theorem: Level repulsion and degenerate eigenvalues
• Non-Weyl asymptotics for quantum graphs with general coupling conditions
• Singular Perturbations and Nonstandard Analysis
• Upper Bounds for the Resonance Counting Function of Schrödinger Operators in Odd Dimensions
• Resonance free regions and non-Hermitian spectral optimization for Schrödinger point interactions
• Spectral analysis of photonic crystals made of thin rods
• Mathematical Theory of Scattering Resonances
• ON EIGENFUNCTIONS OF AN OPERATOR CORRESPONDING TO THE POLES OF THE ANALYTIC CONTINUATION OF THE RESOLVENT THROUGH THE CONTINUOUS SPECTRUM

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