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Browsing by Subject "quantum graphs"

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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.
  • thumbnail.journal.alt
    Item type:Article, Access status: Open Access ,
    On reflectionless equi-transmitting matrices
    (2014) Kurasov, Pavel Borisovič; Ogik, Rao; Rauf, Amar
    Reflectionless equi-transmitting unitary matrices are studied in connection to matching conditions in quantum graphs. All possible such matrices of size 6 are described explicitly. It is shown that such matrices form 30 six-parameter families intersected along 12 five-parameter families closely connected to conference matrices.