Transport characteristics of pure narrow 2D conductors, in which the electron scattering is caused by rough side boundaries, have been studied. The conductance of such strips is highly sensitive to the intercorrelation properties of inhomogeneities of the opposite edges. The case with completely correlated statistically identical boundaries (CCB) is a peculiar one. Herein the electron scattering is uniquely due to fluctuations of the asperity slope and is not related to the strip width fluctuations. Owing to this, the electron relaxation lengths, specifically the localization length, depend quite differently on the asperity parameters as compared to the conductors with arbitrarily intercorrelated edges. The method for calculating the dynamical characteristics of the CCB electron waveguides is proposed clear of the restrictions on the asperity height.

A method is proposed for studying wave and particle transport in disordered waveguide systems of dimension higher than unity by means of exact one-dimensionalization of the dynamic equations in the mode representation. As a particular case, the T = 0 conductance of a two-dimensional quantum wire is calculated, which exhibits ohmic behaviour, with length-dependent conductivity, at any conductor length exceeding the electron quasi-classical mean free path. The unconventional diffusive regime of charge transport is found in the range of conductor lengths where the electrons are commonly considered as localized. In quantum wires with more than one conducting channel, each being identified with the extended waveguide mode, the inter-mode scattering is proven to serve as a phase-breaking mechanism that prevents interference localization without real inelasticity of interaction.PACS numbers: 71.30.+h, 72.15.Rn, natural. Numerous attempts to interpret the results of Ref. 10 within the framework of a single-particle approach were made, in particular, by improving the scaling approach. 9 In this study, however, a fundamentally different strategy is chosen which is an alternative to the RG analysis. 24 We prefer to obtain the observables directly, while conclusions (though indirect) about the localization of electron states are made on the basis of the results.It is instructive to recall that working out, even without a profound spectral analysis, practical asymptotic methods for calculating the disorder-averaged many-particle characteristics (conductivity, density-density correlator, etc.) turned out to be more helpful for the establishment of a highly advanced theory of 1D random systems than the development of rigorous mathematical foundations. [25][26][27][28] The usefulness of such an approach can be attributed to the fact that in the context of the above-mentioned essentially perturbative methods one has managed to trace with the required accuracy the effect of mutual interference of quantum waves corresponding to multiply backscattered current carriers. In such a way, physical results entirely consistent with the anticipations based on mathematical predictions were eventually obtained. The present research was primarily induced by long-standing discontent associated with the lack of arguments of a comparable standard, either in favour of localization or against it, as applied to 2D systems of degenerate electrons subject to a static random potential.Commonly, the presence of inelastic scattering mechanisms is held responsible as a main cause of preventing quantum interference and, thus, Anderson localization. 29 Among these are the electron-phonon and electron-electron interactions and other conceivable methods of energy interchange between the electron bath and the environment. 30 These can lead to the loss of phase (meaning energy) memory or, in other words, phase coherence of electronic states. Note in this connection that in the 1D case the demand of energy coherence admits a large transfer of momentum for onefol...

Transport properties of narrow two-dimensional conducting wires in which the electron scattering is caused by side edges' roughness have been studied. The method for calculating dynamic characteristics of such conductors is proposed which is based on the two-scale representation of the mode wave functions at weak scattering. With this method, fundamentally different by-height and by-slope scattering mechanisms associated with edge roughness are discriminated. The results for single-mode systems, previously obtained by conventional methods, are proven to correspond to the former mechanism only. Yet the commonly ignored by-slope scattering is more likely dominant. The electron extinction lengths relevant to this scattering differ substantially in functional structure from those pertinent to the by-height scattering. The transmittance of ultra-quantum wires is calculated over all range of scattering parameters, from ballistic to localized transport of quasi-particles. The obtained dependence of scattering lengths on the disorder parameters is valid qualitatively for arbitrary inter-correlation of the boundaries' defects.

Starting from the rigorous excitation equation, the propagation of waves through a 2D waveguide with the periodically corrugated finite-length insert is examined in detail. The corrugation profile is chosen to obey the property that its amplitude is small as compared to the waveguide width, whereas the sharpness of the asperities is arbitrarily large. With the aid of the method of mode separation, which was developed earlier for inhomogeneous-in-bulk waveguide systems [Waves Random Media 10, 395 (2000)], the corrugated segment of the waveguide is shown to serve as the effective scattering barrier whose width is coincident with the length of the insert and the average height is controlled by the sharpness of boundary asperities. Due to this barrier, the mode spectrum of the waveguide can be substantially rarefied and adjusted so as to reduce the number of extended modes to the value arbitrarily less than that in the absence of corrugation (up to zero), without changing considerably the waveguide average width.

A rigorous solution for the spectrum of a quasioptical cylindrical cavity resonator with a randomly rough side boundary has been obtained. To accomplish this task, we have developed a method for the separation of variables in a wave equation, which enables one, in principle, to rigorously examine any limiting case-from negligibly weak to arbitrarily strong disorder at the resonator boundary. It is shown that the effect of disorder-induced scattering can be properly described in terms of two geometric potentials, specifically, the "amplitude" and the "gradient" potentials, which appear in wave equations in the course of conformal smoothing of the resonator boundaries. The scattering resulting from the gradient potential appears to be dominant, and its impact on the whole spectrum is governed by the unique sharpness parameter Ξ, the mean tangent of the asperity slope. As opposed to the resonator with bulk disorder, the distribution of nearest-neighbor spacings (NNS) in the rough-resonator spectrum acquires Wigner-like features only when the governing wave operator loses its unitarity, i.e., with the availability in the system of either openness or dissipation channels. It is shown that the reason for this is that the spectral line broadening related to the oscillatory mode scattering due to random inhomogeneities is proportional to the dissipation rate. Our numeric experiments suggest that in the absence of dissipation loss the randomly rough resonator spectrum is always regular, whatever the degree of roughness. Yet, the spectrum structure is quite different in the domains of small and large values of the parameter Ξ. For the dissipation-free resonator, the NNS distribution changes its form with growing the asperity sharpness from poissonian-like distribution in the limit of Ξ≪1 to the bell-shaped distribution in the domain where Ξ≫1.