Localization of waves in a single-mode waveguide with statistically identical rough boundaries

We analyze wave propagation in a narrow 2D waveguide, the properties of which are substantially controlled by wave scattering at random rough boundaries. Usually the opposite side boundaries of the waveguides are considered to have exactly the same or sufficiently close statistical properties. Among all the models of such statistically identical rough boundaries two which are substantially different are distinguished. One of them includes the waveguides with no correlation between the asperities of the opposite edges. Within the other model, correlation between the asperities of the opposite boundaries is exactly the same as the correlation at any waveguide edge. We refer to the boundaries of the latter type as completely correlated (CCB)