Estimates for the lowest eigenvalue of a star graph
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TLDR
In this paper, the authors derived new estimates for the lowest eigenvalue of the Schrodinger operator associated with a star graph in R2 by a variational method and a procedure for identifying test functions which are sympathetic to the geometry of the star graph.About:
This article is published in Journal of Mathematical Analysis and Applications.The article was published on 2009-06-01 and is currently open access. It has received 19 citations till now. The article focuses on the topics: Star (graph theory) & Algebraic connectivity.read more
Citations
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Schrödinger Operators with δ and δ ′-Potentials Supported on Hypersurfaces
TL;DR: In this paper, a self-adjoint Schrodinger operator with δ and δ′-potential supported on a smooth compact hypersurface is defined explicitly via boundary conditions.
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Schr\"odinger operators with delta and delta'-potentials supported on hypersurfaces
TL;DR: In this article, the existence and completeness of the wave operators of the corresponding scattering systems, as well as the unitary equivalence of the singularly perturbed and unperturbed Schrodinger operators are proved.
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Schrödinger operators with δ- and δ′-interactions on Lipschitz surfaces and chromatic numbers of associated partitions
TL;DR: In this paper, the authors investigated Schrodinger operators with δ- and δ′-interactions supported on hypersurfaces, which separate the Euclidean space into finitely many bounded and unbounded Lipschitz domains.
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Schr\"odinger operators with \delta- and \delta'-interactions on Lipschitz surfaces and chromatic numbers of associated partitions
TL;DR: In this article, an operator inequality for Schrodinger operators with δ and δ-interactions was proved for hypersurfaces, which is based on an optimal colouring and involves the chromatic number of the partition.
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Schrödinger operators with δ-interactions supported on conical surfaces
TL;DR: In this paper, the spectral properties of self-adjoint Schrodinger operators with attractive δ-interactions of constant strength α > 0 supported on conical surfaces were investigated and it was shown that the essential spectrum is given by α −+ ∞ [4, ) 2 and that the discrete spectrum is infinite and accumulates to α − 4 2.
References
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Geometrically induced spectrum in curved leaky wires
TL;DR: In this paper, the authors study measure perturbations of the Laplacian in L2(2) supported by an infinite curve in the plane which is asymptotically straight in a suitable sense.
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Leaky Quantum Graphs: A Review
TL;DR: In this article, the authors provide an overview of recent work concerning ''leaky'' quantum graphs described by Hamiltonians given formally by the expression $-\Delta -\alpha \delta (x-Gamma)$ with a singular attractive interaction supported by a graph-like set in $\mathbb{R}^
u,\:
u=2,3$.
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Geometrically induced spectrum in curved leaky wires
TL;DR: In this article, the Laplacian perturbation of the plane with respect to an infinite curve in the plane which is asymptotically straight in a suitable sense is studied.
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Leaky quantum graphs: approximations by point-interaction Hamiltonians
TL;DR: In this paper, an approximation result showing how operators of the type −Δ − γδ(x − Γ) in, where Γ is a graph, can be modelled in the strong resolvent sense by point-interaction Hamiltonians with an appropriate arrangement of the δ potentials.
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Bound states in point-interaction star graphs
TL;DR: In this article, the essential spectrum of the Hamiltonian of a two-dimensional quantum particle interacting with an infinite family of point interactions is discussed, where the latter are arranged into a star-shaped graph with N arms and a fixed spacing between the interaction sites.