  A unified theory for the conductance of a long multimode quantum wire whose
finite segment has randomly rough boundaries is developed. It enables one to
take account of all mechanisms of wave scattering, both related to boundary
roughness and to contacts between the wire rough section and the leads within
the same technical frameworks. The rough part of the conducting wire is shown
to act as a mode-specific randomly modulated effective potential barrier whose
height is governed essentially by the asperity slope. The mean height of the
barrier specifies the number of conducting channels. Under relatively small
asperity amplitude this number can take on arbitrary small values if the
asperities are sufficiently sharp. The channel cut-off that arises when the
asperity sharpness increases can be regarded as a kind of localization, which
is not related to the disorder but rather is of entropic origin. The
fluctuating part of the barrier results in two fundamentally different types of
guided wave scattering, viz., inter- and intramode scattering. The intermode
scattering is shown to be for the most part very strong except in the cases of
(a) extremely smooth asperities, (b) excessively small length of the corrugated
segment, and (c) the asperities sharp enough for only one conducting channel to
remain in the wire. Under strong intermode scattering, a new set of conducting
channels develops, which have the form of decoupled extended modes subject to
individual random potentials. In view of this fact, two transport regimes only
are realizable in randomly corrugated multimode wires, specifically, the
ballistic and the localized regime, the latter characteristic of
one-dimensional random systems. Two kinds of localization are thus shown to
coexist in waveguide-like systems with randomly corrugated boundaries,
specifically, the entropic localization and the one-dimensional Anderson
localization.
