The WIgner ENSemble MC (WIENS) was announced a year ago as a union of theoretical and numerical approaches, algorithms, and an experimental code for the Wigner simulation of nanostructures. The foremost objective was to demonstrate that two-dimensional Wigner simulations are not an impossible computational task. The desired convergence was observed at the expense of long computational times. It has been concluded that the approach cannot present a challenge to the well-established deterministic methods of coherent transport in two-dimensional devices. The approach is, however, the core of a general particle scheme, which is able to handle the case of two-dimensional quantum transport with dissipation.
WIENS has recently been theoretically extended for the special limiting cases where transport is nearly coherent or is dominated by processes of dissipation. The underlying idea is to assume knowledge of the solution to the transport equation in the considered limiting case and to consider the equation for the corresponding correction. The latter is given by the difference between the Wigner-Boltzmann and the coherent Wigner functions, if the phonon interaction is weak when compared to the potential variations involved, and between the Wigner-Boltzmann and the Boltzmann functions, if the transport is nearly classical. Several numerical advantages are expected from this treatment. The correction is by assumption small, which reduces the required precision. The corresponding equation describes the evolution of an initial condition, as the contact injection terms cancel in the process of derivation. The a priori information needs to be interfaced with other numerical approaches which are more efficient in obtaining the limiting solution. In particular, the coherent Wigner solution can be provided by a Green's function approach, which is quite effective for coherent cases. The thereby established interface to alternative simulation approaches involves collaboration with groups from the home and international institutions.