It has been known for many years that the Boltzmann equation provides a good description of the transport coefficients for a dilute gas of particles interacting with short-range forces. While this equation for the phase space (or Wigner) distribution function f(r, p, t) is closed, the rigorous mechanical evolution equation for f is not according to the investigation of Bogoliubov, Born and Green, Kirkwood, Yvon and others.D, 2 l Recently many efforts have been made to derive and generalize the former equation from the latter by introducing approximations.ll,3J Unfortunately. most of the approximations previously proposed by various authors seem to be motivated by mathematical tractability rather than by physical reasoning. To this category of approximations belong e. g. Bogoliubov's ffunctional dependence assumption on the many-body distribution functions,ll the factorizability of the initial many-body density into one-body densities, 3 l, <11fJ) I,where p(t) is a many-particle density operator, .Q the volume; I11CJl > and <11

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With the help of quantum-scattering-theory methods and the approximation of stationary phase, a one-dimensional coherent random-walk model which describes both tunneling and scattering above the potential diffusion of particles in a periodic one-dimensional lattice is proposed. The walk describes for each lattice cell, the time evolution of modulating amplitudes of two opposite-moving Gaussian wave packets as they are scattered by the potential barriers. Since we have a coherent process, interference contributions in the probabilities bring about strong departures from classical results. In the near-equilibrium limit, Fick’s law and its associated Landauer diffusion coefficient are obtained as the incoherent contribution to the quantum current density along with a novel coherent contribution which depends on the lattice properties as [(1−R)/R]1/2.