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On the controllability of quantum transport in an electronic nanostructure. (English) Zbl 1326.37013

The paper addresses the problem of the controllability for the model of the quantum transport. The model is based on a coupled system of the linear Schrödinger equation for the electron wave function, self-consistently coupled to the Poisson equation for the respective electrostatic field. The model corresponds to the traditional transistor setup, with the control voltage applied at a boundary segment which corresponds to the transistor’s gate. The analysis produces a rigorous proof of the controllability of this scheme. As a generalization, a nonlinear version of the model is considered too. In that case, the Poisson equation includes the local source created by the electron density.

MSC:

37C20 Generic properties, structural stability of dynamical systems
35Q40 PDEs in connection with quantum mechanics
82D80 Statistical mechanics of nanostructures and nanoparticles
82D37 Statistical mechanics of semiconductors
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