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...