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arXiv · 1012.3634

On the electron scattering on the one-dimensional complexes: the vertex amplitudes method

Alexander F. Klinskikh·Anton V. Dolgikh·Peter A. Meleshenko·Sergey A. Sviridov
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Abstract

The problem of electron scattering on the one-dimensional complexes is considered. We propose a novel theoretical approach to solution of the transport problem for a quantum graph. In the frame of the developed approach the solution of the transport problem is equivalent to the solution of a linear system of equations for the \emph{vertex amplitudes} $\mathbf{\Psi}$. All major properties, such as transmission and reflection amplitudes, wave function on the graph, probability current, are expressed in terms of one $\mathbf{\Gamma}$-matrix that determines the transport through the graph. The transmission resonances are analyzed in detail and comparative analysis with known results is carried out.

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Alexander F. Klinskikh, Anton V. Dolgikh, Peter A. Meleshenko, Sergey A. Sviridov. 2010-12-16. On the electron scattering on the one-dimensional complexes: the vertex amplitudes method. https://arxiv.org/abs/1012.3634

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