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

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

2010-12-16

arxiv.org/abs/1012.3634v2

Physics

Mathematical Physics

14 pages, 15 figures

Scientific paper

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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