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This is nowadays an interesting and fast-developing field of mathematical physics, not only because of its intrinsic mathematical interest, but also in view of the remarkable applications to nanoelectronic devices modeling. The recent progresses in semiconductor engineering, in fact, make it possible to build ultra-small semiconductor structures in which the quantum effects on the charge carriers not only are no more negligible but, on the contrary, constitute the basis of  the devices functioning. An accurate mathematical description of the quantum transport in such quantum devices becomes necessary in  order to perform numerical simulation, which allow to reduce laboratory time and expenses, to simulate peculiar working conditions and to optimize device parameters.

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