Date of Original Version
We calculated transport coefficients in thin films in which the particle wavelength is comparable to the thickness of the film, and the motion across the film is quantized. The perturbative calculations are analytical almost to the very end, and result in explicit transparent expressions for the transport coefficients via the correlation function of surface inhomogeneities, density of particles, and film thickness. The final results are given for Gaussian correlations of the surface inhomogeneities. The discrete nature of the spectrum leads to a non-analyticity of transport coefficients as a function of particle density and film thickness, especially for degenerate fermions. Surface inhomogeneity causes both in-band scattering and interband transitions; the role of interband transitions is determined by the correlation radius of surface inhomogeneities. The shape of the curves for the dependence of transport coefficients on the number of particles and film thickness is determined by the correlation of surface inhomogeneities and is not very sensitive to their amplitude. For short-range correlations, the interband transitions lead to a saw-like shape of the curves. With an increasing correlation radius, the interband transitions become suppressed, and the saw teeth gradually decrease, reducing, in the end, to small kinks on otherwise monotonic curves. Careful analysis of the transition from quantum to semiclassical and classical regimes allowed us to improve the accuracy of our previous classical calculations.
Meyerovich, A. E., & Stepaniants, S. (1997). Ballistic Transport in Ultrathin Films with Random Rough Walls J.Phys.:Condens.Matter., 9, 4157. doi: 10.1088/0953-8984/9/20/015
Available at: http://dx.doi.org/10.1088/0953-8984/9/20/015