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Lyapunov exponents for schrödinger operators with random, but deterministic potentials

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

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References

  1. J. Avron, B. Simon: Almost periodic Schrödinger operators: I. Limit periodic potentials; Commun. Math. Phys. 82 (1982), 101–120

    Article  MathSciNet  MATH  Google Scholar 

  2. I. Herbst, J. Howland: The Stark ladder and other one-dimensional external field problems; Commun. Math. Phys. 80 (1981), 23

    Article  MathSciNet  MATH  Google Scholar 

  3. W. Kirsch: On a class of random Schrödinger operators, to appear in Adv. in Appl. Math.

    Google Scholar 

  4. W. Kirsch: A remark on the behavior of the eigenvalues of the Laplacian and bounded domains under small perturbations.

    Google Scholar 

  5. W. Kirsch, F. Martinelli: On the spectrum of Schrödinger operators with a random potential; Commun. Math. Phys. 85 (1982), 329–350

    Article  MathSciNet  MATH  Google Scholar 

  6. W. Kirsch, F. Martinelli: On the ergodic properties of the spectrum of general random operators, J. Reine Angew. Math. 334, (1982), 141–156

    MathSciNet  MATH  Google Scholar 

  7. W. Kirsch, F. Martinelli: On the essential selfadjointness of stochastic Schrödinger operators; Duke Math. J. 50 (1983), 1255–1260

    Article  MathSciNet  MATH  Google Scholar 

  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. Poincaré

    Google Scholar 

  9. S. Kotani: Lyapunov indices determine absolutely continuous spectra of stationary random one-dimensional Schrödinger operators; Proc. Stoch. Anal. Kyoto 1982

    Google Scholar 

  10. S. Kotani: Support theorems for random Schrödinger operators; Commun. Math. Phys. 97, 443–452

    Google Scholar 

  11. H. Kunz, B. Souillard: Sur le spectre des operateurs aux differences finies aleatoires; Commun. Math. Phys. 78 (1980), 201–246

    Article  MathSciNet  MATH  Google Scholar 

  12. S. Nakao: On the spectral distribution of the Schrödinger operator with random potential; Japan. J. Math. 3 (1977), 111–139

    MathSciNet  MATH  Google Scholar 

  13. M. Reed, B. Simon: Methods of Modern Mathematical Physics, Vol. IV, Academic Press 1978

    Google Scholar 

  14. B. Simon: Kotani theory for one dimensional stochastic Jacobi matrices; Commun. Math. Phys. 89 (1983) 227

    Article  MathSciNet  MATH  Google Scholar 

  15. B. Simon: Semiclassical analysis of low lying eigenvalues III. Width of the ground state band in strongly coupled solids, Caltech-Preprint

    Google Scholar 

  16. B. Souillard: Contribution to the Workshop on Lyapunov exponents.

    Google Scholar 

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Ludwig Arnold Volker Wihstutz

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© 1986 Springer-Verlag

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Kirsch, W. (1986). Lyapunov exponents for schrödinger operators with random, but deterministic potentials. In: Arnold, L., Wihstutz, V. (eds) Lyapunov Exponents. Lecture Notes in Mathematics, vol 1186. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0076842

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  • DOI: https://doi.org/10.1007/BFb0076842

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-16458-6

  • Online ISBN: 978-3-540-39795-3

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