On a discrete model for quantum transport in semi-conductor devices

We introduce a semi-discretized version of the Wigner equation. The model fulfills the following fundamental requirements: it is well-posed in a natural functional framework; as the mesh size of the discretization goes to 0, the solutions converge (with spectral accuracy) to the solution of the continuous equation; it is consistent with the semi-classical limit. We also discuss an operator splitting implementation of this model.