Ballistic transport in narrow channels and films

Abstract

We present a simple description of ballistic transport in systems with random rough walls. All characteristic parameters, including the mean free path and localization length, are expressed explicitly via the correlation function (correlation length R and amplitude l) of surface inhomogeneities. Scattering by surfaces inhomogeneities in channels with width L creates a new mesoscopic transport length of the order of (L2R/l2) f (R/λ). The function f has a minimum when the particle wavelength λ ~ R. The transport problem includes possible quantization of motion across the channel. The calculations are performed with the help of canonical coordinate transformation which reduces a transport problem with rough random walls to an exactly equivalent problem with ideal flat walls, but with random bulk distortion. Applications include transport in thin films, porous media, localization and slip effects, etc.