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Remark on the absence of absolutely continuous spectrum ford-dimensional Schrödinger operators with random potential for large disorder or low energy

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Abstract

We show that there is no absolutely continuous part in the spectrum of the Anderson tight-binding model for large disorder or low energy. The proof is based on the exponential decay of the Green's function proved by Fröhlich and Spencer. The extension of this result to the continuous case is also discussed.

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References

  1. Anderson, P.: Absence of diffusion in certain random lattices. Phys. Rev.109, 1492 (1958)

    Google Scholar 

  2. Pastur, L.A.: Spectral properties of disordered systems in the one body approximation. Commun. Math. Phys.75, 179 (1980)

    Google Scholar 

  3. Kunz, H., Souillard, B.: Sur le spectre des opérateurs aux différences finies aléatoires. Commun. Math. Phys.78, 201 (1980)

    Google Scholar 

  4. Fröhlich, J., Spencer, T.: Absence of diffusion in the Anderson tight binding model for large disorder or low energy. Commun. Math. Phys.88, 151 (1983)

    Google Scholar 

  5. Berezanskii, M.: Expansion in eigenfunction of self adjoint operators. In: Translation of mathematical monographs, Vol. 17, A.M.S. (1968)

  6. Simon, B.: Schrödinger semigroups. Bull. Am. Math. Soc.7, 447 (1983)

    Google Scholar 

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

    Google Scholar 

  8. Holden, H., Martinelli, F.: On the absence of diffusion near the bottom of the spectrum for a random Schrödinger operator onL 2(R v). Commun. Math. Phys.93, 197 (1984)

    Google Scholar 

  9. Wegner, F.: Bounds on the density of states in disordered systems. Z. Phys. B44, 9 (1981)

    Google Scholar 

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Author notes

  1. F. Martinelli

    Present address: Dipartimento di Matematica, Università di Trento, I-38050, Povo, Trento, Italy

  2. E. Scoppola

    Present address: Dipartimento di Fisica, Università “La Sapienza” Piazzale A. Moro, 2, I-00185, Roma, Italy

Authors and Affiliations

  1. Laboratoire de Physique Théorique et Hautes Energies, Université Pierre et Marie Curie, 4 Place Jussieu, F-75230, Paris Cedex 05, France

    F. Martinelli & E. Scoppola

Authors
  1. F. Martinelli
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  2. E. Scoppola
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Additional information

Communicated by T. Spencer

Laboratoire associé au CNRS- LA280

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Martinelli, F., Scoppola, E. Remark on the absence of absolutely continuous spectrum ford-dimensional Schrödinger operators with random potential for large disorder or low energy. Commun.Math. Phys. 97, 465–471 (1985). https://doi.org/10.1007/BF01213410

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  • DOI: https://doi.org/10.1007/BF01213410

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