BALLISTIC TRANSPORT IN ULTRA-THIN FILMS WITH RANDOM ROUGH WALLS

We calculated transport coefficients in thin films in which the partic le wavelength is comparable to the thickness of the film, and the moti on across the film is quantized. The perturbative calculations are ana lytical almost to the very end, and result in explicit transparent exp ressions for the transport coefficients via the correlation function o f surface inhomogeneities, density of particles, and film thickness. T he final results are given for Gaussian correlations of the surface in homogeneities. The discrete nature of the spectrum leads to a non-anal yticity of transport coefficients as a function of particle density an d film thickness, especially for degenerate fermions. Surface inhomoge neity causes both in-band scattering and interband transitions; the ro le of interband transitions is determined by the correlation radius of surface inhomogeneities. The shape of the curves for the dependence o f transport coefficients on the number of particles and film thickness is determined by the correlation of surface inhomogeneities and is no t 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 suppr essed, and the saw teeth gradually decrease, reducing, in the end, to small kinks on otherwise monotonic curves. Careful analysis of the tra nsition from quantum to semiclassical and classical regimes allowed us to improve the accuracy of our previous classical calculations.