Equilateral Quantum Graphs and Their Decorations
نویسنده
چکیده
We consider magnetic Schrödinger operators on quantum graphs with identical edges. The spectral problem for the quantum graph is reduced to the discrete magnetic Laplacian on the corresponding combinatorial graph and a certain Hill equation. This may be viewed as a generalization of the classical spectral analysis for the Hill operator to such structures. Using this correspondence we show that that the number of gaps in the spectrum of Schrödinger operators in graphs admits an estimate from below in terms of the Hill operator independently of the graph structure. We also discuss the decoration of graphs in the context of this correspondence.
منابع مشابه
Spectra of Schrödinger operators on equilateral quantum graphs
We consider magnetic Schrödinger operators on quantum graphs with identical edges. The spectral problem for the quantum graph is reduced to the discrete magnetic Laplacian on the underlying combinatorial graph and a certain Hill operator. In particular, it is shown that the spectrum on the quantum graph is the preimage of the combinatorial spectrum under a certain entire function. Using this co...
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