Electron scattering by nanotube Y-junction. Computation and application to modeling by graphs

We demonstrate a possibility to compute the intensity of electron transport through Y-type junctions of three-dimensional metallic nanotubes. Keeping in mind an asymptotic modeling of reliable nanostructures by quantum graphs, we conjecture that scattering matrix of a graph should be the same as scattering matrix of its nanosize-prototype. The numerical computation of the latter allows a way to determine the "gluing" conditions at a graph. Exploring this conjecture we show that commonly used gluing conditions for graphs are normally not adequate.