Nonlinear conduction properties of multiport quantum waveguide-based devices are theoretically investigated. A two dimensional finite element solver for the time independent Schrödinger equation combined with Poisson equation has been developed. It handles arbitrary geometrical designs and potential profiles in the device active zone. Starting from transmission spectra calculated out of equilibrium, current–voltage characteristics of a quantum branch line directional coupler are derived as a function of the chemical potential of the injection region and of the applied bias between the input and output terminals of the structure. Under the approximation of ballistic transport, a detailed analysis of mono- and multimode propagation regimes shows that pronounced negative differential conductance effects combined with real space lateral transfers can be obtained. The robustness of the current–voltage characteristics as a function of temperature is also addressed. © 2000 American Institute of Physics.