IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v113y1982i1p173-202.html
   My bibliography  Save this article

A new approach to the problem of disordered harmonic chains

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/0378437182900140
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
    File URL: https://libkey.io/10.1016/0378-4371(82)90014-0?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Durand-Vidal, Serge & Turq, Pierre & Bernard, Olivier & Treiner, Claude & Blum, Lesser, 1996. "New perspectives in transport phenomena in electrolytes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 231(1), pages 123-143.
    2. Calvo, Miguel, 1991. "The character of the metastable phase singularities near the spinodal line," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 177(1), pages 339-344.
    3. Günther, C.C.A. & Rikvold, P.A. & Novotny, M.A., 1994. "Application of a constrained-transfer-matrix method to metastability in the d = 2 Ising ferromagnet," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 212(1), pages 194-229.
    4. Binder, K., 1986. "Decay of metastable and unstable states: Mechanisms, concepts and open problems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 140(1), pages 35-43.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:phsmap:v:113:y:1982:i:1:p:173-202. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.