Resonances in one-dimensional disordered systems: Localization of energy and resonant transmission

Localized states in one-dimensional, open, disordered systems and their connection to the internal structure of random samples have been studied. It is shown that the localization of energy and anomalously high transmission associated with these states are due to the existence inside the sample of a transparent (for a given resonant frequency) segment with minimum size of the order of the localization length. An analogy between the stochastic scattering problem at hand and a deterministic quantum problem permits one to describe analytically some statistical properties of localized states with high transmission. It is shown that there is no one-to-one correspondence between the localization and high transparency: only a small fraction of the localized modes exhibit a transmission coefficient close to one. The maximum transmission is provided by the modes that are localized in the center, while the highest energy concentration occurs in cavities shifted towards the input. An algorithm is proposed to estimate the position of an effective resonant cavity and its pumping rate by measuring the resonant transmission coefficient. The validity of the analytical results is checked by extensive numerical simulations and wavelet analysis.