Méhats, Florian; Privat, Yannick; Sigalotti, Mario On the controllability of quantum transport in an electronic nanostructure. (English) Zbl 1326.37013 SIAM J. Appl. Math. 74, No. 6, 1870-1894 (2014). 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. Reviewer: Boris A. Malomed (Tel Aviv) Cited in 5 Documents 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 Keywords:Schrödinger equation; Poisson equation; transistor model PDFBibTeX XMLCite \textit{F. Méhats} et al., SIAM J. Appl. Math. 74, No. 6, 1870--1894 (2014; Zbl 1326.37013) Full Text: DOI arXiv