Quantum graph vertices with permutation-symmetric scattering probabilities |
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Authors: | Ond?ej Turek Taksu Cheon |
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Affiliation: | Laboratory of Physics, Kochi University of Technology, Tosa Yamada, Kochi 782-8502, Japan |
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Abstract: | Boundary conditions in quantum graph vertices are generally given in terms of a unitary matrix U. Observing that if U has at most two eigenvalues, then the scattering matrix S(k) of the vertex is a linear combination of the identity matrix and a fixed Hermitian unitary matrix, we construct vertex couplings with this property: For all momenta k, the transmission probability from the j-th edge to ?-th edge is independent of (j,?), and all the reflection probabilities are equal. We classify these couplings according to their scattering properties, which leads to the concept of generalized δ- and δ′-couplings. |
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Keywords: | Scattering matrix Singular vertex Equal transmission Quantum wire |
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