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Connections between the electron eigenstates and conductivity ofone-dimensional disordered electron systems is studied in the framework of thetight-binding model. We show that for weak disorder only part of the statesexhibit resonant transmission and contribute to the conductivity. The rest ofthe eigenvalues are not associated with peaks in transmission and theamplitudes of their wave functions do not exhibit a significant maxima withinthe sample. Moreover, unlike ordinary states, the lifetimes of these `hidden'modes either remain constant or even decrease (depending on the coupling withthe leads) as the disorder becomes stronger. In a wide range of the disorderstrengths, the averaged ratio of the number of transmission peaks to the totalnumber of the eigenstates is independent of the degree of disorder and is closeto the value $\sqrt{2/5}$, which was derived analytically in theweak-scattering approximation. These results are in perfect analogy to thespectral and transport properties of light in one-dimensional randomlyinhomogeneous media, which provides strong grounds to believe that theexistence of hidden, non-conducting modes is a general phenomenon inherent to1D open random systems, and their fraction of the total density of states isthe same for quantum particles and classical waves.

Transmission Resonances Anomaly in 1D Disordered Quantum Systems