Disorder-induced mutation of quasi-normal modes in 1D open systems

We study the relation between quasi-normal modes (QNMs) and transmission resonances (TRs) in one-dimensional (1D) disordered systems. We show that while each maximum in the transmission coefficient is always related to a QNM, the reverse statement is not necessarily correct. There exists an intermediate state, where only part of the QNMs are localized and provide a resonant transmission. The rest of QNMs (strange modes) are not localized and not associated with any anomalies in the transmission. The ratio of the number of the normal QNMs to the total number of QNMs is independent of the type of disorder, and varies slightly in rather wide ranges of the strength of a single scattering and the length of the random sample.