The absence of localization in one-dimensional disordered harmonic chains

We study one-dimensional harmonic chains in which clusters of two or three defect atoms are embedded randomly. The disorder in the systems appears in the masses of the atoms. Reflectionless modes are obtained by studying different kinds of correlation among the masses. The localization behaviour of the modes around these special frequencies is examined analytically as well as numerically. To discern the nature of the modes at and around those frequencies, density of states, bandwidth scaling and site Green functions are studied. If the special frequencies lie within the common band of the constituent atoms and at zero the modes are extended at and around them. However, the modes are critical when the special frequency appears at the upper band edge of the host system. The number of non-scattered modes is estimated for all cases. It is approximately square root N for the dimer problem. For the trimer problem with degenerate resonances appearing inside the constituent band it is approximately N 3 4 /. If the degenerate resonances of the trimer appear at zero frequency the number of non-scattered modes is approximately N 5 6/.