Skip to main content
Log in

Localization for random and quasiperiodic potentials

  • Articles
  • Published:
Journal of Statistical Physics Aims and scope Submit manuscript

Abstract

A survey is made of some recent mathematical results and techniques for Schrödinger operators with random and quasiperiodic potentials. A new proof of localization for random potentials, established in collaboration with H. von Dreifus, is sketched.

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. I. Goldsheid, S. Molchanov, and L. Pastur,Funct. Anal. Appl. 11:1 (1977).

    Google Scholar 

  2. P. Anderson,Phys. Rev. 109:1492 (1958).

    Google Scholar 

  3. T. Spencer, inCritical Phenomena, Random Systems and Gauge Theories, K. Osterwalder and R. Stora, eds. (North-Holland, 1986).

  4. B. Simon and T. Wolff,Commun. Pure Appl. Math. 39:75 (1986).

    Google Scholar 

  5. F. Delyon, Y. Levy, and B. Souillard,Commun. Math. Phys. 100:21 (1985).

    Google Scholar 

  6. H. Furstenberg,Trans. Am. Math. Soc. 108:377 (1963).

    Google Scholar 

  7. I. M. Lifshitz,Sov. Phys. Usp. 7:549 (1965).

    Google Scholar 

  8. W. Kirsch and F. Martinelli,Commun. Math. Phys. 89:27 (1983).

    Google Scholar 

  9. M. Reed and B. Simon,Methods of Modern Mathematical Physics IV (Academic Press, New York, 1978).

    Google Scholar 

  10. J. Fröhlich and T. Spencer,Commun. Math. Phys. 88:151 (1983).

    Google Scholar 

  11. J. Fröhlich, F. Martinelli, E. Scoppola, and T. Spencer,Commun. Math. Phys. 101:21 (1985).

    Google Scholar 

  12. H. von Dreifus, NYU. Thesis, Part 2.

  13. J. Chayes and L. Chayes, inCritical Phenomena, Random Systems and Gauge Theories, K. Osterwalder and R. Stora, eds. (North-Holland, 1986).

  14. F. Wegner,Z. Phys. B 44:9 (1981).

    Google Scholar 

  15. E. Dinaburg and Ya. Sinai,Funct. Anal. Appl. 9:279 (1975).

    Google Scholar 

  16. S. Aubry,Solid State Sci. 8:264 (1978).

    Google Scholar 

  17. M. Herman,Comm. Math. Helv. 58:453 (1983).

    Google Scholar 

  18. J. Avron and B. Simon,Duke J. 50:369 (1983).

    Google Scholar 

  19. F. Delyon,J. Phys. A 20:L21 (1987).

    Google Scholar 

  20. J. Bellissard, R. Lima, and D. Testard,Commun. Math. Phys. 88:207 (1983).

    Google Scholar 

  21. J. Fröhlich, T. Spencer, and P. Wittwer, preprint.

  22. Ya. Sinai,J. Stat. Phys. 46 (1987).

  23. S. Surace, NYU. Thesis.

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Spencer, T. Localization for random and quasiperiodic potentials. J Stat Phys 51, 1009–1019 (1988). https://doi.org/10.1007/BF01014897

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01014897

Key words

Navigation