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

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 existing theoretical results, the asymptotic model is explicitly adapted to physically realistic situations and numerical results are shown in various cases.