Resumen de Global controllability of the 1D Schrödinger–Poisson equation

Mariano De Leo, Constanza Sánchez Fernández de la Vega, Diego Rial

• This paper is concerned with both the local and global internal controllability of the 1D Schrödinger–Poisson equation iut(x,t)=−uxx+V(u)u, which arises in quantum semiconductor models. Here V(u) is a Hartree-type nonlinearity stemming from the coupling with the 1D Poisson equation, which includes the so-called doping profile or impurities. More precisely, it is shown that for both attractive and repulsive self-consistent potentials —depending on the balance between the total charge and the impurities— this problem is globally internal controllable in a suitable Sobolev space.