Wigner Paths Method in Quantum Transport with Dissipation

The concept of Wigner paths in phase space both provides a pictorial representation of the quantum evolution of the system of interest and constitutes a useful tool for numerical solutions of the quantum equation describing the time evolution of the system. A Wigner path is defined as the path followed by a “simulative particle” carrying a σ-contribution of the Wigner function through the Wigner phase-space, and is formed by ballistic free flights separated by scattering processes (both scattering with phonons and with an arbitrary potential profile can be included), as for the case of semiclassical particles. Thus, the integral transport equation can be solved by a Monte Carlo technique by means of simulative particles following classical trajectories, in complete analogy to the “Weighted Monte Carlo” solution of the Boltzmann equation in the integral form.