Generalized Weyl–Wigner formalism for the simulation of open quantum devices: a density-matrix approach

A density-matrix approach for the description of quantum-transport phenomena in systems with open boundaries is proposed. We shall show that the application of the conventional Wigner-function formalism within a source-term boundary-condition scheme leads to unphysical results, such as injection of coherent electronic states from the contacts. To overcome such basic limitations, we propose a generalization of the standard Weyl–Wigner formulation. The latter can be regarded as a quantum mechanical derivation of the phenomenological injection model commonly employed in the simulation of open quantum devices.