Internal controllability of some equation arising in quantum semiconductor model

by Prof. Mariano De Leo (Universidad Nacional de General Sarmiento, Buenos Aires)

Thursday 10 Feb 2011, 16:00 → 17:00 Europe/Rome

Aula Conversi (Dip. di Fisica - Edificio G. Marconi)

In this talk we shall be concerned with both the local and global internal controllability of the 1D Schroedinger-Poisson equation which arises in quantum semiconductor models. Here the potential has a Hartree-type nonlinearity stemming from the coupling with the 1D Poisson equation, which includes the so-called doping profile or impurities, given by a compactly supported regular function C. More precisely, we shall show that for both attractive and repulsive self-consistent potentials - depending on the balance between the total charge, which is a conserved quantity, and the impurities - this problem is globally internal controllable in the Sobolev space.