Effect of scattering by random surface inhomogeneities on transport along the walls and localization in ultrathin systems is analyzed. A simple universal surface collision operator is derived outside of the quantum resonance domain. This operator contains all relevant information on statistical and geometrical characteristics of weak roughness and can be used as a general boundary condition on the corrugated surfaces. In effect, the boundary problem for the three-dimensional ͑3D͒ transport equation is replaced by the explicit matrix collision operator coupling a set of 2D transport equations. This operator is applied to a variety of systems including ultrathin films and channels with rough walls, particles adsorbed on or bound to rough substrates, multilayer systems with randomly corrugated interfaces, etc. The main emphasis is on quantization of motion between the walls, though the quasiclassical limit is considered as well. The diffusion and mobility coefficients, localization length, and other parameters are expressed analytically or semianalytically via the intrawall and interwall correlation functions of surface corrugation. ͓S0163-1829͑99͒00935-2͔

A rigorous perturbative transport equation for ballistic particles in thin films with random rough walls is derived by the diagrammatic Keldysh technique for both quasiclassical and quantized motion across the film. The derivation is based on canonical Migdal transformation that replaces a transport problem with random rough walls by an equivalent problem with flat boundaries and randomly distorted bulk. The rigorous derivation requires a modification of our previously used transformation to avoid non-Hermitian perturbations. The unusual nondiagonal structure of the effective scattering operator makes the transport equation different from the standard Waldmann-Snider equation when the distance between quantized levels for the motion across the film is comparable to the wall-induced perturbation. Outside of this anomalous quantum resonance region, the transport equation is similar to that for scattering by bulk impurities. The magnitude of the anomaly is calculated for degenerate particles and Gaussian correlations of surface inhomogeneities. The transport problem is solved analytically for the single-band occupancy and in the limiting cases of very large and very small correlation radii of inhomogeneities for an arbitrary correlation function of surface roughness. Elsewhere, the transport equation is analyzed numerically for the Gaussian correlation function. Transport coefficients are expressed explicitly via the angular harmonics of the surface correlation function; in the anomalous region, the results contain certain supplemental correlators. The results reveal various effects of interwall correlations on transport including an oscillatory dependence on the number of occupied minibands. The transition from quantum to quasiclassical description of ballistic motion across the ͑thick͒ film can be hindered by residual interwall interference effects similar to those in classical optic problems for thick films without bulk attenuation. Erroneous matrix elements in our previous calculations have been corrected. ͓S0163-1829͑98͒05943-8͔

The interference between boundary and bulk scattering processes is analyzed for ultrathin films with random rough walls. The effective collision and transport relaxation times for scattering by random bulk and surface inhomogeneities are calculated, when possible analytically, in quantum size effect conditions. The transport and localization results are expressed via the bulk transport parameters and statistical characteristics of the surface corrugation.The diagrammatic calculation includes second order effects for boundary scattering and full summation for bulk processes. The interference contribution is large in systems with robust bulk scattering and can be comparable, or even exceed, the pure wall contribution to the transport coefficients.

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An interaction of a linear surface gravity wave with weakly irregular one-dimensional bathymetry has been analyzed using the diagrammatic technique. The Boltzmann diffusion coefficient and the Anderson localization length for the wave energy density are expressed analytically via a correlation function of irregularities of the sea floor. The results are applied to different topographies. The effect of a finite region of irregularities, viscous damping, wave interaction, current, geometrically diffuse wave source, and anisotropy on localization is briefly discussed. The theory provides a scenario for the observation of large scale Anderson localization phenomenon in a tank or possibly in coastal waters.