85 citations
- Czech Academy of Sciences, Nuclear Physics InstituteCZ65 papers
- University Frères Mentouri Constantine 1DZ31 papers
- Czech Academy of SciencesCZ25 papers
- Durban University of TechnologyZA25 papers
- Université Constantine 2DZ25 papers
- Akdeniz UniversityTR24 papers
- Czech Technical University in PragueCZ21 papers
- University of ShahroodIR21 papers
- FZU ‒ Institute of Physics of the Academy of Sciences of the Czech RepublicCZ17 papers
- Institute of Mathematics with Computer CenterRU15 papers
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8 papers · 1 filter
Exotic eigenvalues and analytic resolvent for a graph with a shrinking edge
Gregory Berkolaiko, Denis I. Borisov, Marshall King
We consider a metric graph consisting of two edges, one of which has length which we send to zero. On this graph we study the resolvent and spectrum of the Laplacian…
A geometric approximation of -interactions by Neumann Laplacians
Andrii Khrabustovskyi, Olaf Post
We demonstrate how to approximate one-dimensional Schrödinger operators with -interaction by a Neumann Laplacian on a narrow waveguide-like domain. Namely, we consider a domain…
Analyticity of resolvents of elliptic operators on quantum graphs with small edges
D. I. Borisov
We consider an arbitrary metric graph, to which we glue another graph with edges of lengths proportional to , where is a small positive parameter. On suc…
On finitely many resonances emerging under distant perturbations in multi-dimensional cylinders
D. I. Borisov, A. M. Golovina
We consider a general elliptic operator in an infinite multi-dimensional cylinder with several distant perturbations; this operator is obtained by ``gluing'' several single perturb…
Spectral localization for quantum Hamiltonians with weak random delta interaction
Denis I. Borisov, Matthias Taeufer, Ivan Veselic
We consider a negative Laplacian in multi-dimensional Euclidean space (or a multi-dimensional layer) with a weak disorder random perturbation. The perturbation consists of a sum of…
Spectral asymptotics of the Laplacian on Platonic solids graphs
Pavel Exner, Jiri Lipovsky
We investigate the high-energy eigenvalue asymptotics quantum graphs consisting of the vertices and edges of the five Platonic solids considering two different types of the vertex…