WIGNER PATHS FOR ELECTRONS INTERACTING WITH PHONONS

Wigner trajectories in phase space provide a pictorial representation of the quantum evolution of a system of interest in the Wigner-functio n formulation of quantum mechanics with many analogies with the descri ption of classical evolutions. The existence of Wigner trajectories ha s been discussed so far only for ballistic coherent electrons moving i n an external potential profile. We prove in this paper the existence of Wigner paths that are defined also in the presence of electron-phon on coupling, and go over some interpretative problems related to Wigne r trajectories. Wigner paths can be used to determine the evolution of the Wigner function in time during scattering processes. This general result opens new fields of application of the concept of Wigner funct ion, mainly in connection with the numerical study of quantum transpor t in mesoscopic systems.