Quantized systems with randomly corrugated walls and interfaces

Abstract

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

Interference of bulk and boundary scattering in films with a quantum size effect

“…Independently, S. Stepaniants and one of the authors [29] and, later, Bratkovsky and Rashkeev [30] introduced the relevant Migdal-like transformation and performed explicit transport and localization calculations for ballistic systems (see also Refs. [26,27] and references therein; similar transformation was also used in Ref. [31] for calculation of the QSE spectrum in rough contacts).…”

“…Without this large term, one could use the transport equation of Refs. [26,27] for QSE systems in the second order in the surface distortion e. Here, one needs a different equation, which is still of the second order in e but contains the full summation of the impurity terms with U.…”

“…The extension to other systems can be done in the same way as it has been done in Ref. [27] for quantized ballistic systems without bulk scattering.…”

Surface roughness and size effects in quantized films

“…11 Recently, we developed a transparent semianalytical formalism for transport in systems with rough boundaries that allows simple uniform calculations in a wide range of parameters and for various types of roughness with and without bulk scattering. [12][13][14] This formalism unites approaches by Tesanovic et al, 15 Fishman and Calecki, 16 Kawabata, 17 Meyerovich and S. Stepaniants, 18 and Makarov et al 19 ͑for a brief comparison between different theoretical approaches see Refs. 13 and 20͒.…”

Beams of gravitationally bound ultracold neutrons in rough waveguides

“…[11] and references therein) in which the experimental results are linked explicitly to the parameters of the surface roughness. Note that there is also an alternative theoretical approach to the same experiment [12], which, however, does not reveal such an explicit link.…”