Tripartite connection condition for quantum graph vertex

Abstract

We discuss formulations of boundary conditions in a quantum graph vertex and demonstrate that the so-called $ST$-form can be further reduced up to a form more effective in certain applications: In particular, in identifying the number of independent parameters for given ranks of two connection matrices, or in calculating the scattering matrix when both matrices are singular. The new form of boundary conditions, called the $PQRS$-form, also gives a natural scheme to design generalized low and high pass quantum filters.

LaTeX Elsevier format, 10 pages, 2 figures

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Cited by in corpus (5)

• Periodic quantum graphs from the Bethe-Sommerfeld perspective
• Hermitian unitary matrices with modular permutation symmetry
• Vertex coupling in quantum graphs: approximations by scaled Schroedinger operators
• Inverse scattering problem for quantum graph vertices
• Quantizing graphs, one way or two?