On discrete spectrum of a model graph with loop and small edges

DOI10.1007/S10958-021-05503-2zbMath1472.81069OpenAlexW3197460965MaRDI QIDQ1983985

A. I. Mukhametrakhimova, M. N. Konyrkulzhaeva, Denis I. Borisov

Publication date: 13 September 2021

Published in: Journal of Mathematical Sciences (New York) (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10958-021-05503-2

Mathematics Subject Classification ID

Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) (34L40) Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.) (05C70) Eigenfunctions, eigenfunction expansions, completeness of eigenfunctions of ordinary differential operators (34L10) Boundary eigenvalue problems for ordinary differential equations (34B09) Quantum mechanics on special spaces: manifolds, fractals, graphs, lattices (81Q35)

Related Items (2)

Resolvent of a Schrödinger operator on a model graph with small loops ⋮ Taylor series for resolvents of operators on graphs with small edges

Cites Work

• Unnamed Item
• On a model graph with a loop and small edges. Holomorphy property of resolvent
• Quantum graphs with small edges: holomorphy of resolvents
• Limits of quantum graph operators with shrinking edges
• Perturbation of threshold of the essential spectrum of the Schrödinger operator on the simplest graph with a small edge
• Scale invariant effective Hamiltonians for a graph with a small compact core
• Approximation of a general singular vertex coupling in quantum graphs
• Homogenization of elasticity problems on singular structures
• Simplest graphs with small edges: asymptotics for resolvents and holomorphic dependence of spectrum

This page was built for publication: On discrete spectrum of a model graph with loop and small edges