On an open transient Schrödinger-Poisson system

International audienceA mathematical model of quantum transient transport in dimension d = 2, 3 is derived and analyzed. The model describes the evolution of electrons injected into the device by reservoirs having a stationary statistics. The electrostatic potential in the device is modified by electron presence through electrostatic interaction. The wave functions are computed in the device region and satisfy non homogeneous open boundary conditions at the device edges. A priori estimates are deduced from the “dissipative properties” of the boundary conditions and from the repulsive character of the electrostatic interaction