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arXiv · 1312.6075

Quantum graph vertices with minimal number of passbands

Sergey S. Poghosyan·Taksu Cheon
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Abstract

We study a set of scattering matrices of quantum graphs containing minimal number of passbands, i.e., maximal number of zero elements. The cases of even and odd vertex degree are considered. Using a solution of inverse scattering problem, we reconstruct boundary conditions of scale-invariant vertex couplings. Potential-controlled universal flat filtering properties are found for considered types of vertex couplings. Obtained boundary conditions are approximated by simple graphs carrying only $δ$ potentials and inner magnetic field.

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Sergey S. Poghosyan, Taksu Cheon. 2014-02-20. Quantum graph vertices with minimal number of passbands. https://doi.org/10.7566/jpsj.83.044004

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