A Space Dependent Wigner Equation Including Phonon Interaction

The quantum transport in far from equilibrium conditions is determined not only by the nanostructure potential, but also by dissipative processes due to interaction with phonons. Of interest is the reduced Wigner function fw r p t , which is obtained by taking the trace over the phonon coordinates. We present an equation for the reduced Wigner function which is obtained after a hierarchy of approximations. The equation treats the coherent part of the transport imposed by the nanostructure potential at a rigorous quantum level. It is general enough to account for the quantum effects in the interaction with phonons. The relevant quantum effects are collision broadening associated with the lack of energy conservation in the scattering process, collision retardation due to the memory character of the equation and the intra-collisional field effect, the action of the field during the collision process.