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Browsing by Subject "scattering theory"

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  • thumbnail.journal.alt
    Item type:Article, Access status: Open Access ,
    Geometric properties of quantum graphs and vertex scattering matrices
    (2010) Kurasov, Pavel; Nowaczyk, Marlena
    Differential operators on metric graphs are investigated. It is proven that vertex matching (boundary) conditions can be successfully parameterized by the vertex scattering matrix. Two new families of matching conditions are investigated: hyperplanar Neumann and hyperplanar Dirichlet conditions. Using trace formula it is shown that the spectrum of the Laplace operator determines certain geometric properties of the underlying graph.