Periodic and Random Systems

Abstract

One the fundamental properties of periodic systems concerns absolute continuity of their spectra guaranteeing a natural transport through such structures. This is discussed here for the particular case of a periodically curved waveguide. It does not exhaust interesting features of such systems: the spectral structure is discussed in the example of periodic point perturbations of tubes and layers, also in presence of a magnetic field. On the other hand, randomness leads to localization, at least at the bottom of the spectrum; this is illustrated here on example of a tube with a randomly corrugated boundary.