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The vibrations of a chain of diatomic molecules with glasslike disorder are examined using a perturbation theory in configuration space rather than wave-number space (i.e., a perturbed Einstein model). The frequency spectrum is found from the solution of two simultaneous polynomial equations. As a test, this theory is applied to the special case of the monatomic chain, and a comparison of the results is made with the direct numerical calculation of Dean. Good agreement is obtained.
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Wu et al. (1969) studied this question.
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