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barrier is compared with one corresponding to a finite periodic chain of $N$ potential barriers or wells. It is proved, that even for small periodic potentials the exponential decreasing of the transmission coefficient for growing $N$ takes place in lacunas of the corresponding periodic operator on the whole real line. Using the Landauer formula we express the conductivity of the... [Report]

A two-dimensional junction is modelled by a quantum graph with a resonance hode. The boundary condition at the node is calculated from the frirst principles . In low temperators limit for simplest T-junction it coincides with the the boundary condition suggested by Datta. The free parameter contained in Datta's condition is interpreted in spectral terms of an intermediate Hamiltonian. The... [Report]