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Eigenfunctions in a Two-Particle Anderson Tight Binding Model

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Abstract

We establish the phenomenon of Anderson localisation for a quantum two-particle system on a lattice \({\mathbb{Z}^d}\) with short-range interaction and in presence of an IID external potential with sufficiently regular marginal distribution.

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References

  1. Aizenman M.: Localization at weak disorder: some elementary bounds. Rev. Math. Phys. 6, 1162–1184 (1994)

    Article  MathSciNet  Google Scholar 

  2. Aizenman, M., Warzel, S.: Localization bounds for multiparticle systems. Commun. Math. Phys., arXiv: math-ph/0809.3436, 2008

  3. Aizenman M., Molchanov S.A.: Localization at large disorder and extreme energies: An elementary derivation. Commun. Math. Phys. 157, 245–278 (1993)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  4. Aizenman M., Schenker J.H., Friedrich R.M., Hundertmark D.: Finite-Volume Fractional-Moment Criteria for Anderson Localization. Commun. Math. Phys. 224, 219–253 (2001)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  5. Aizenman, M., Warzel, S.: Lecture Notes on Random Schröger Operators, in preparation

  6. Berezanskii, J.M.: Expansion in eigenfunctions of self-adjoint operators. Transl. Math. Monographs 17. Providence, R.I.: Amer. Math. Soc. 1968

  7. Chulaevsky V., Suhov Y.: Wegner bounds for a two-particle tight binding model. Commun. Math. Phys. 283, 479–489 (2008)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  8. Chulaevsky, V., Suhov, Y.: Eigenfunctions in a two-particle Anderson tight binding model. In preparation

  9. von Dreifus H., Klein A.: A new proof of Localization in the Anderson Tight Binding Model. Commun. Math. Phys. 124, 285–299 (1989)

    Article  MATH  ADS  Google Scholar 

  10. Fröhlich J., Spencer T.: Absence of diffusion in the Anderson tight binding model for large disorder or low energy. Commun. Math. Phys. 88, 151–184 (1983)

    Article  MATH  ADS  Google Scholar 

  11. Fröhlich J., Martinelli F., Scoppola E., Spencer T.: A constructive proof of localization in Anderson tight binding model. Commun. Math. Phys. 101, 21–46 (1985)

    Article  MATH  ADS  Google Scholar 

  12. Goldsheid I.Ya., Molchanov S.A., Pastur L.A.: A pure point spectrum of the one dimensional Schrödinger operator. Funct. Anal. Appl. 11, 1–10 (1977)

    Article  Google Scholar 

  13. Kunz H., Souillard B.: Sur le spectre des opérateurs aux différences finies aléatoires. Commun. Math. Phys. 78, 2011–246 (1980)

    Article  MathSciNet  Google Scholar 

  14. Simon B.: Schrödinger semigrooups. Bull. Amer. Math. Soc. 7, 447 (1983)

    Article  Google Scholar 

  15. Stollmann P.: Wegner estimates and localization for continuous Anderson models with some singular distributions. Arch. Math. 75, 307–311 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  16. Stollmann, P.: Caught by disorder. Basel-Boston: Birkhäuser, 2001

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Authors and Affiliations

  1. Département de Mathématiques et d’Informatique, Université de Reims, Moulin de la Housse, B.P. 1039, 51687, Reims Cedex 2, France

    Victor Chulaevsky

  2. Department of Pure Mathematics and Mathematical Statistics, University of Cambridge, Wilberforce Road, Cambridge, CB3 0WB, UK

    Yuri Suhov

Authors
  1. Victor Chulaevsky
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  2. Yuri Suhov
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Correspondence to Victor Chulaevsky.

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Communicated by B. Simon

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Chulaevsky, V., Suhov, Y. Eigenfunctions in a Two-Particle Anderson Tight Binding Model. Commun. Math. Phys. 289, 701–723 (2009). https://doi.org/10.1007/s00220-008-0721-0

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  • DOI: https://doi.org/10.1007/s00220-008-0721-0

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