Compatibility of Landauer diffusion coefficient with classical transport theory

Mesoscopic diffusion in the ballistic regime has long been recognized to be described by the non-local Landauer diffusion coefficient: D=cLT/(2R). This is an incoherent result because, in its derivation, the quantum interference between incident and scattered waves has been neglected. This raises the question as to whether or not it may be derived from a purely classical theory such as Boltzmannʹs transport equation. We prove that the answer is positive. We show that in spite of the fact that the Boltzmann and the incoherent quantum theory are described by different diffusive stochastic processes and have different local diffusion coefficients, they give the same algebraic expression (the Landauer result) for the non-local diffusion coefficient