Localization of the vibrational states of binary disordered linear chains

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Abstract
We present the results of computer experiments to determine the localization of the eigenstates of a harmonic disordered linear chain with equal nearest-neighbor force constants and differing mass ratios, concentrations, and degrees of short-range order among two constituent atoms. We examine two measures of localization, the spatial extent of the modes and the decay length of the modes away from the region of appreciable strength. Experimentally, the two measures are found to agree at low frequencies but to behave oppositely at peaks of the impurity band. A one-particle Green's-function theory for the decay parameter is developed and is in good agreement with the experimental decay length in disordered chains. The same theory is applied to the decay of forced vibrations outside the bands of perfectly ordered chains.