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Singular behavior of the density of states and the Lyapunov coefficient in binary random harmonic chains

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Abstract

We study the integrated density of statesH(ω 2) of a chain of harmonic oscillators with a binary random distribution of the masses. We show in particular that there is a dense set of values of the squared frequency for which the differenceH(ω 2+ɛ)-H(ω 2) has a singularity of the type ¦ɛ¦2α, multiplied by a periodic function of ln ¦ɛ¦, where the exponent α and the period depend continuously onω 2. In the region where α < 1/2,H is not differentiate on a dense set of points. The same type of singularities is also present in the Lyapunov coefficient.

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Authors and Affiliations

  1. Institute for Theoretical Physics, Princetonplein 5, P.O. Box 80.006, 3508 TA, Utrecht, The Netherlands

    Th. M. Nieuwenhuizen

  2. Service de Physique Théorique, CEN de Saclay, B.P.2, F 91191, Gif-sur-Yvette Cedex, France

    J. M. Luck

Authors
  1. Th. M. Nieuwenhuizen
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  2. J. M. Luck
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Nieuwenhuizen, T.M., Luck, J.M. Singular behavior of the density of states and the Lyapunov coefficient in binary random harmonic chains. J Stat Phys 41, 745–771 (1985). https://doi.org/10.1007/BF01010002

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  • DOI: https://doi.org/10.1007/BF01010002

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