Square-gradient mechanism of surface scattering in quasi-1D rough waveguides

We develop a perturbative approach that allows one to study the surface scattering in quasi-1D waveguides with rough boundaries. Our approach is based on the construction of an effective ``bulk'' potential of a very complicated structure. The detailed analysis of this potential reveals that apart from the well known terms considered in the previous studies, one should keep specific terms that depend on the square of the derivative of the boundaries. As was found, in spite of an apparent smallness of these square-gradient scattering (SGS) terms, there is a physically important region of parameters, in which they can not be neglected. Our approach also demonstrates that the contribution of the SGS-mechanism of scattering strongly depends on the type of the rough boundaries (uncorrelated, symmetric or antisymmetric)