MERCREDI 20 OCTOBRE 2010 14 heures Salle Séminaire 5 Centre de Physique Théorique Marseille-Luminy Andrea Mantile USTV, Toulon Title: An explicit model for the adiabatic evolution of quantum observables driven by 1D shape resonances. Abstract: Our work is concerned with a linearized version of the quantum transport problem where the Schrdinger-Poisson operator is replaced by a non-autonomous Hamiltonian, slowly varying in time. We consider an explicitly solvable system where a semiclassical island is described by a flat potential barrier, while a time dependent delta interaction is used as a model for a single quantum well. Introducing, in addition to the complex deformation, a further modi...cation formed by arti...cial interface conditions, we give a reduced equation for the adiabatic evolution of the sheet density of charges accumulating around the interaction point. (Joint work with: A. Farj and F. Nier)