Wigner function for identical particles

In the last decades it has become clear that a rigorous quantum approach to electron transport in nano-device design is necessary, not only for the solution of problems where quantum effects are essential but also for testing the semiclassical approximation by comparison with exact quantum results obtained for the very same system. The Wigner-function approach seems to be the most appropriate method to deal with space dependent problems since it explicitely refers to variables defined in an (r,p) Wigner "phase space". This paper extends the Wigner-function approach to quantum transport developed for the single electron case to a more complicated system of n indistinguishable particles. In particular, we study how the Monte Carlo technique and the Wigner paths method can be applied to a single-particle Wigner function defined for a system of n interacting particles. Starting from the definition of the one particle Wigner function as the Fourier transform of the two point G/sup \n\n\t\t