Classical and quantum nonlinear localized excitations in discrete systems

Discrete breathers, or intrinsic localized modes, are spatially localized, time--periodic, nonlinear excitations that can exist and propagate in systems of coupled dynamical units. Recently, some experiments show the sighting of a form of discrete breather that exist at the atomic scale in a magnetic solid. Other observations of breathers refer to systems such as Josephson--junction arrays, photonic crystals and optical-switching waveguide arrays. All these observations underscore their importance in physical phenomena at all scales. The authors review some of their latest theoretical contributions in the field of classical and quantum breathers, with possible applications to these widely different physical systems and to many other such as DNA, proteins, quantum dots, quantum computing, etc.