Far from equilibrium steady states of 1D-Schrödinger-Poisson systems with quantum wells II

Virginie Bonnaillie-Noël (1) , Francis Nier (1) , Yassine Patel (1)

1 IRMAR - Institut de Recherche Mathématique de Rennes

This article continues the asymptotic analysis of a nonlinear Schrödinger-Poisson system which models in a far from equilibrium regime the quantum transport in electronic devices like resonant tunneling diodes. Within the reduction to an h-dependent linear problem with uniform regularity estimates for the potential already established in the first part, explicit computations of the asymptotic finite dimensional nonlinear system are derived. They rely on an accurate (phase-space) analysis of the tunnel effect which relies on some kind of Breit-Wigner formula and Fermi golden rule.

Mots clés: Schrödinger-Poisson system; Asymptotic analysis; Multiscale problems

Domaines: Equations aux dérivées partielles [math.AP]; Physique mathématique [math-ph]; Physique mathématique [math-ph]

Virginie Bonnaillie-Noël, Francis Nier, Yassine Patel. Far from equilibrium steady states of 1D-Schrödinger-Poisson systems with quantum wells II. 2007. ⟨hal-00124705v1⟩