Global controllability of 1D Schroedinger-Poisson equation

Abstract

This paper is concerned with both the local and global internal controllability of the 1D Schroedinger-Poisson equation i u_t = -u_xx +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 prole 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.