Lyapunov exponents for schrödinger operators with random, but deterministic potentials

Part III: Random Schrödinger operators. Wave Propagation in Random Media
Part of the Lecture Notes in Mathematics book series (LNM, volume 1186)


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    J. Avron, B. Simon: Almost periodic Schrödinger operators: I. Limit periodic potentials; Commun. Math. Phys. 82 (1982), 101–120MathSciNetCrossRefzbMATHGoogle Scholar
  2. [2]
    I. Herbst, J. Howland: The Stark ladder and other one-dimensional external field problems; Commun. Math. Phys. 80 (1981), 23MathSciNetCrossRefzbMATHGoogle Scholar
  3. [3]
    W. Kirsch: On a class of random Schrödinger operators, to appear in Adv. in Appl. Math.Google Scholar
  4. [4]
    W. Kirsch: A remark on the behavior of the eigenvalues of the Laplacian and bounded domains under small perturbations.Google Scholar
  5. [5]
    W. Kirsch, F. Martinelli: On the spectrum of Schrödinger operators with a random potential; Commun. Math. Phys. 85 (1982), 329–350MathSciNetCrossRefzbMATHGoogle Scholar
  6. [6]
    W. Kirsch, F. Martinelli: On the ergodic properties of the spectrum of general random operators, J. Reine Angew. Math. 334, (1982), 141–156MathSciNetzbMATHGoogle Scholar
  7. [7]
    W. Kirsch, F. Martinelli: On the essential selfadjointness of stochastic Schrödinger operators; Duke Math. J. 50 (1983), 1255–1260MathSciNetCrossRefzbMATHGoogle Scholar
  8. [8]
    W. Kirsch, S. Kotani, B. Simon: Absence of absolutely continuous spectrum for some one dimensional random but deterministic Schrödinger operators; to appear in Anal. I.H. PoincaréGoogle Scholar
  9. [9]
    S. Kotani: Lyapunov indices determine absolutely continuous spectra of stationary random one-dimensional Schrödinger operators; Proc. Stoch. Anal. Kyoto 1982Google Scholar
  10. [10]
    S. Kotani: Support theorems for random Schrödinger operators; Commun. Math. Phys. 97, 443–452Google Scholar
  11. [11]
    H. Kunz, B. Souillard: Sur le spectre des operateurs aux differences finies aleatoires; Commun. Math. Phys. 78 (1980), 201–246MathSciNetCrossRefzbMATHGoogle Scholar
  12. [12]
    S. Nakao: On the spectral distribution of the Schrödinger operator with random potential; Japan. J. Math. 3 (1977), 111–139MathSciNetzbMATHGoogle Scholar
  13. [13]
    M. Reed, B. Simon: Methods of Modern Mathematical Physics, Vol. IV, Academic Press 1978Google Scholar
  14. [14]
    B. Simon: Kotani theory for one dimensional stochastic Jacobi matrices; Commun. Math. Phys. 89 (1983) 227MathSciNetCrossRefzbMATHGoogle Scholar
  15. [15]
    B. Simon: Semiclassical analysis of low lying eigenvalues III. Width of the ground state band in strongly coupled solids, Caltech-PreprintGoogle Scholar
  16. [16]
    B. Souillard: Contribution to the Workshop on Lyapunov exponents.Google Scholar

Copyright information

© Springer-Verlag 1986

Authors and Affiliations

  1. 1.Institut für MathematikRuhr-Universität BochumBochumFed. Rep. of Germany

Personalised recommendations