Landauer diffusion coefficient: A classical result

Abstract

Using the classical version of the $S$-matrix scattering theory, we develop a stochastic process called persistent random walk. We show that the one-channel Landauer diffusion coefficient can be obtained from a purely incoherent classical theory. The time dependent mesoscopic diffusion current satisfies a Maxwell-Cattaneo relation. Therefore the time dependent mesoscopic diffusion process is described by the telegrapher's equation.