Skip to main content
SpringerLink
Log in

A central limit theorem for the disordered harmonic chain

  • Published:
Communications in Mathematical Physics Aims and scope Submit manuscript

Abstract

Using methods introduced by Furstenberg and Tutubalin we prove a central limit theorem for the amplitudes of plane waves travelling in a semi-infinite isotopically disordered harmonic chain. This theorem is applied to the problem of heat conduction in disordered harmonic chains.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Furstenberg, H.: Trans. A.M.S.,108, 377 (1963)

    Google Scholar 

  2. Tutubalin, V. N.: Theory Probability Appl.10, 15 (1965);13, 65 (1958)

    Google Scholar 

  3. Nagaev, S. V.: Theory Probability Appl.2, 378 (1957)

    Google Scholar 

  4. Dunford, N., Schwartz, J.: Linear operators, pt. I. New York: Interscience 1958

    Google Scholar 

  5. Ahlfors, L. V.: Complex analysis. New York: McGraw Hill 1966

    Google Scholar 

  6. Lebowitz, J. L.: Phys. Rev.114, 1192 (1959)

    Google Scholar 

  7. Casher, A., Lebowitz, J. L.: J. Math. Phys.12, 1701 (1971)

    Google Scholar 

  8. Matsuda, H., Ishii, K.: Suppl. Prog. Theor. Phys.45, 231 (1970)

    Google Scholar 

  9. Ishii, K.: Suppl. Prog. Theor. Phys.53, 77 (1973)

    Google Scholar 

  10. Rubin, R. J., Greer, W.: J. Math. Phys.12, 1686 (1971)

    Google Scholar 

  11. Yoshioka, Y.: Proc. Japan Academy49, 665 (1973)

    Google Scholar 

  12. O'Connor, A. J., Lebowitz, J. L.: J. Math. Phys.15, 692 (1974)

    Google Scholar 

  13. Schmidt, H.: Phys. Rev.105, 425 (1957)

    Google Scholar 

  14. Borland, R. E.: Proc. Roy. Soc. (London) A.274, 529 (1963)

    Google Scholar 

  15. Halperin, B. I.: Advances in Chemical Physics13, 123 (1967)

    Google Scholar 

  16. Hori, J.: Spectral Theory of Disordered Chains and Lattices. Oxford: Pergamon, 1968

    Google Scholar 

  17. Feller, W.: Introduction to probability theory and its applications, II. New York: Wiley 1966

    Google Scholar 

  18. Maradudin, A. A., Montroll, E. W., Weiss, G. H.: Theory of lattice dynamics in the harmonic approximation. New York: Academic Press 1968

    Google Scholar 

  19. Bell, R. J.: Reports on Progress in Physics35, 1315 (1972)

    Google Scholar 

  20. Kato, T.: Perturbation theory for linear operators. Berlin-Heidelberg-New York: Springer 1966

    Google Scholar 

  21. Peierls, R. E.: Quantum Theory of Solids, Oxford 1965

Download references

Author information

Authors and Affiliations

  1. Faculty of Mathematics, Open University, Walton Hall, MK7 6AA, Milton Keynes, England

    A. J. O'Connor

Authors
  1. A. J. O'Connor
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Communicated by J. L. Lebowitz

Rights and permissions

Reprints and permissions

About this article

Cite this article

O'Connor, A.J. A central limit theorem for the disordered harmonic chain. Commun.Math. Phys. 45, 63–77 (1975). https://doi.org/10.1007/BF01609867

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01609867

Keywords

Search

Navigation