Schrödinger operators with almost periodic potemntial: An overview

  • J. Bellissard
Conference paper
Part of the Lecture Notes in Physics book series (LNP, volume 153)


Periodic Potential Random Operator Pure Point Pure Point Spectrum Bloch Electron 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [AA]
    ANDRE G., AUBRY S., Proceedings of the VIIIth International Colloquium on Group Theoretical Methods in Physics, L.P. Horowitz, Y. Nee'man Ed., Tel Aviv (1979).Google Scholar
  2. [AS]a)
    AVRON J., SIMON B., Phys. Rev. Lett. 46 (1981) 1166.Google Scholar
  3. [AS]b)
    Almost Periodic Schrödinger Operator I & II (I, submitted to C.M.P.), Caltech Preprint 1981.Google Scholar
  4. [AS]c)
    Cantor Sets and Schrödinger Operators: Transcient and Recurrent Spectrum, Caltech Preprint 1980, to appear in J. Funct. Anal.Google Scholar
  5. [B]
    BLOCH A.N., in Lecture Notes in Physics, no° 6, (1977).Google Scholar
  6. [BT]a)
    BELLISSARD J., TESTARD D., in Proceedings of the Kingston Conference on Operator Algebra, 1980.Google Scholar
  7. [BT]b)
    Almost Periodic Hamiltonians: an Algebraic Approach, Preprint Marseille CPT-81/P.1311, submitted to C.M.P.Google Scholar
  8. [BFLT]a)
    BELLISSARD J., FORMOSO A., LIMA R., TESTARD D., A Quasi-Periodic Interaction with Metal Insulator Transition, to appear in Phys. Rev. B.Google Scholar
  9. [BFLT]b)
    On the Almost Periodic Kronig Penney Model, Marseille Preprint 1981.Google Scholar
  10. [BLT]
    BELLISSARD J., LIMA R., TESTARD D., Almost Random Operators: K-Theory and Spectral Properties, in preparation.Google Scholar
  11. [B.S.]
    BELLISSARD J., SCOPPOLA E., The Density of States of Almost Periodic Hamiltonian and the Frequency Module: A Counter-Example, Marseille Preprint 1981, submitted to C.M.P.Google Scholar
  12. [BH]
    BERTHIER A.M., HERMANN M.R., Private communication and work in preparation.Google Scholar
  13. [BH]
    CHULAEVSKY V.H., On the Perturbation of Schrödinger Operators with Periodic Potentials, (1981), to appear in Uspekh. Math. Nauk.Google Scholar
  14. [C]a)
    CONNES A., in Lecture Notes in Mathematics, no° 725 (1979).Google Scholar
  15. [C]b)
    Adv. Math. 39, 31 (1981).Google Scholar
  16. [DS]
    DINABURG E.I., SINAI Ya.G., Funct. Anal. and Appl. 9, 279 (1976).Google Scholar
  17. [DMN]
    DOBRUVIN B.A., MATVEEV V.B., NOVIKOV S.P., Russ. Mat. Sur. 1, 59 (1976).Google Scholar
  18. [E]
    ELLIOTT G., Lecture given at the Oberwolfhart Meeting on K-Theory, October 1981.Google Scholar
  19. [F]
    FRÖHLICH H., Proc. Roy. Soc. A223, 296 (1954).Google Scholar
  20. [G]
    GORDON A.Ya., Usp. Math. Nauk. 31, 257 (1976).Google Scholar
  21. [H]
    HOFSTADTER D.R., Phys. Rev. B14, 2239 (1976).Google Scholar
  22. [J]
    JEROME D., MAZAUD A., RIBAULT M., SCHULZ H.J., BECHGAARD K., in J. Phys. (Paris) 42, 991 (1981).Google Scholar
  23. [L]
    LITTLE W.A., Phys. Rev. A134, 1416 (1964).Google Scholar
  24. [M]a)
    MOSER J., An Example of a Schrödinger Operator with Almost Periodic Potential and Nowhere Dense Spectrum, ETH Preprint (1980).Google Scholar
  25. [M]b)
    To appear, ETH Preprint 1981.Google Scholar
  26. [P]
    PASTUR L.A., Russ. Math. Survey 28 (1), 1 (1973).Google Scholar
  27. [Pe]a)
    PEIERLS R.S., Z. Phys. 80, 763 (1933).Google Scholar
  28. [Pe]b)
    Quantum Theory of Solids, Oxford, Clarendon Press (1955).Google Scholar
  29. [R]
    RAUH A., Phys. Status Sol. B65, K131 (1974), B69, K9 (1975).Google Scholar
  30. [Sa]
    SARNAK P., Spectral Behaviour of Quasi-Periodic Potential, New York University Preprint, 1981.Google Scholar
  31. [S]
    SIMON B., A review of the subject will appear in Rev. Mod. Phys.Google Scholar
  32. [Sh]
    SHUBIN M.A., Russ. Math. Survey 33 (2) 1 (1978).Google Scholar

Copyright information

© Springer-Verlag 1982

Authors and Affiliations

  • J. Bellissard
    • 1
  1. 1.Université de Provence et Centre de Physique Théorique, CNRSMarseille

Personalised recommendations