Ballistic localization in quasi-one-dimensional waveguides with rough surfaces

Structure of eigenstates in a periodic quasi-one-dimensional waveguide with a rough surface is studied both analytically and numerically. We have found a large number of “regular” eigenstates for any high energy. They result in a very slow convergence to the classical limit in which the eigenstates are expected to be completely ergodic. As a consequence, localization properties of eigenstates originated from unperturbed transverse channels with low indexes are strongly localized (delocalized) in the momentum (coordinate) representation. These eigenstates were found to have a quite unexpected form that manifests a kind of “repulsion” from the rough surface. Our results indicate that standard statistical approaches for ballistic localization in such waveguides seem to be inappropriate.