Novel resonant processes in one-dimensional elastic scattering

The effect of ordered and disordered arrays on resonant elastic scattering is considered by using some simple properties of the propagator. A crucial role is played by the residues at the complex poles which define the resonant eigenstates. The main effect of disorder near resonance energy is to modify the coupling of the resonant eigenstate with the end points of the system. This may lead to situations where decay occurs through the incident direction resulting in the almost disappearance of the transmission peak. The results throw light on the formation process of localized and extended states in single systems. (author)