Computing the steady states for an asymptotic model of quantum transport in resonant heterostructures

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

1 IRMAR - Institut de Recherche Mathématique de Rennes

In this article we propose a rapid method to compute the steady states, including bifurcation diagrams, of resonant tunneling heterostructures in the far from equilibrium regime. Those calculations are made on a simplified model which takes into account the characteristic quantities which arise from an accurate asymptotic analysis of the nonlinear Schrödinger-Poisson system. After a summary of the former theoretical results, the asymptotical model is explicitly adapted to physically realistic situations and numerical results are shown in various cases. UNE VERSION MODIFIEE DE CE TEXTE EST PARUE DANS J. COMPUT. PHYS.

Mots clés: Schrödinger-Poisson system; resonant tunneling diode; asymptotic model

Domaines: Analyse numérique [math.NA]; Equations aux dérivées partielles [math.AP]

Virginie Bonnaillie-Noël, Francis Nier, Mamodyasine Patel. Computing the steady states for an asymptotic model of quantum transport in resonant heterostructures. 2005. ⟨hal-00012708⟩