Abstract
We study some aspects of the effect of mass disorder on the spectrum of the dynamical matrix of an infinite crystal in the harmonic approximation. Under suitable conditions on the masses, it is shown that the spectrum contains an absolutely continuous part and a nonempty set of isolated point eigenvalues of finite multiplicity whose number is smaller than or equal to the number of impurity atoms if the latter is finite. These conditions are satisfied only in the limiting case of zero concentration of each species of impurity. We draw some conjectures and make remarks on the spectrum under less restrictive conditions on the masses and briefly compare them with known results for random harmonic systems.
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Supported in part by the Swiss National Fund (to M.R.) and the Eidgenössische Stipendienkommission für ausländische Studierende (to W. F. W.).
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Romerio, M., Wreszinski, W.F. On the spectrum of the dynamical matrix for a class of disordered harmonic systems. J Stat Phys 17, 301–310 (1977). https://doi.org/10.1007/BF01014400
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DOI: https://doi.org/10.1007/BF01014400