Ballistic transport in nanostructures: Explicity solvable models

Abstract

The theory of self-adjoint operator extensions is applied to the construction of a sufficiently large class of exactly solvable ballistic transport models in nanostructures. In the models obtained, the transmission coefficient T(E) demonstrates a simple dependence on the parameters of the modeled device and the external magnetic field. Examples are given of the models of quantum dots in which T(E), and thus the conductance, exhibit an oscillatory behavior.