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This paper presents an analytical study of the coexistence of differenttransport regimes in quasi-one-dimensional surface-disordered waveguides (orelectron conductors). To elucidate main features of surface scattering, thecase of two open modes (channels) is considered in great detail. Main attentionis paid to the transmission in dependence on various parameters of the modelwith two types of rough-surface profiles (symmetric and antisymmetric). It isshown that depending on the symmetry, basic mechanisms of scattering can beeither enhanced or suppressed. As a consequence, different transport regimescan be realized. Specifically, in the waveguide with symmetric roughboundaries, there are ballistic, localized and coexistence transport regimes.In the waveguide with antisymmetric roughness of lateral walls, another regimeof the diffusive transport can arise. Our study allows to reveal the role ofthe so-called square-gradient scattering which is typically neglected inliterature, however, can give a strong impact to the transmission.

Ballistic, diffusive, and localized transport in surface-disordered systems: Two-mode waveguide