  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.
