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A new approach to the problem of disordered harmonic chains

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  • Nieuwenhuizen, T.M.

Abstract

In the problem of harmonic chains with random masses the exponential growth rate and the spectral distribution function are shown to be the real and imaginary part of Dyson's characteristic function along its cut in the complex plane. A new function — satisfying a certain integral equation — is introduced from which the characteristic function follows immediately. The functions introduced by Dyson, Schmidt and Matsuda and Ishii are recovered as special cases and it is shown that Schmidt's distributions WN converge as N →∞. Relations between Dyson's and Schmidt's functions are obtained. Finally the same method is applied to the problem of harmonic chains with random variables Kn⧸mn and Kn+1⧸mn and to the tight binding electron model with random site energies.

Suggested Citation

  • Nieuwenhuizen, T.M., 1982. "A new approach to the problem of disordered harmonic chains," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 113(1), pages 173-202.
    • Handle: RePEc:eee:phsmap:v:113:y:1982:i:1:p:173-202
    DOI: 10.1016/0378-4371(82)90014-0
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    References listed on IDEAS

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    1. Cassell, E.J. & Lebowitz, M.D. & Wolter, D.W. & McCarroll, J.R., 1971. "Health and the urban environment. IX. The concept of the multiplex independent variable," American Journal of Public Health, American Public Health Association, vol. 61(12), pages 2348-2353.
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    Cited by:

    1. Garibotti, C.R. & Martiarena, M.L. & Zanette, D.H., 1990. "Singularities in the nonisotropic Boltzmann equation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 165(3), pages 361-369.

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