Transport in Channels and Films with Rough Surfaces. II. Quantized Motion of Ballistic Particles

Abstract

This is the second in the series of papers on transport phenomena along random rough surfaces. We apply our simple general approach\cite{r1} to transport in very narrow channels, when the particles wavelength is comparable to the width of the channels and the motion across the channel is characterized by discrete quantum states. The discrete nature of the spectrum leads to a non-analyticity of transport coefficients as a function of thickness or channel width, especially for degenerate fermions. Surface inhomogeneity leads to both on-level scattering and interlevel transitions. As in\cite{r1}, transport coefficients are expressed explicitly via the correlation function of surface inhomogeneities. The shape of the curves for the dependence of transport coefficients on the number of particles and/or film thickness is determined by the correlation radius of surface inhomogeneities and is not sensitive to their amplitude. For short range correlations, the curves assume a saw-like shape as a result of the interlevel transitions. With increasing correlation radius, the interlevel transitions loose their importance, and the saw teeth gradually decrease, reducing, in the end, to simple kinks on practically monotonic curves. Applications include Gaussian and short-range $δ$-type correlations. Careful analysis of the transition from quantum to semi-classical and classical regimes allowed us to improve the accuracy of our previous classical calculations. PACS numbers: 72.10.Bg, 73.20.Fz, 73.50.Bk, 79.20.Rf