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Journal of Statistical Physics

, Volume 147, Issue 1, pp 194–205 | Cite as

Dynamical Localization of the Chalker-Coddington Model far from Transition

  • Joachim Asch
  • Olivier Bourget
  • Alain Joye
Article

Abstract

We study a quantum network percolation model which is numerically pertinent to the understanding of the delocalization transition of the quantum Hall effect. We show dynamical localization for parameters corresponding to edges of Landau bands, away from the expected transition point.

Keywords

Localization Length Unitary Restriction Resolvent Estimate Random Unitaries Matrix Element Decay 
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.

Notes

Acknowledgements

We gratefully acknowledge support from the grants: Fondecyt Grant 1080675; MATH-AmSud, 09MATH05; Scientific Nucleus Milenio ICM P07-027-F; ECOS-CONICYT C10E01; Elementary Particles Latino American NETwork.

References

  1. 1.
    Aizenman, M., Elgart, A., Naboko, S., Schenker, J., Stolz, G.: Moment analysis for localization in random Schrödinger operators. Invent. Math. 163, 343–413 (2006) MathSciNetADSzbMATHCrossRefGoogle Scholar
  2. 2.
    Aizenman, M., Molchanov, S.: Localization at large disorder and at extreme energies: an elementary derivation. Commun. Math. Phys. 157, 245–278 (1993) MathSciNetADSzbMATHCrossRefGoogle Scholar
  3. 3.
    Aizenman, M., Warzel, S.: Resonant delocalization for random Schrödinger operators on tree graphs. http://arxiv.org/abs/1104.0969v2 (2011)
  4. 4.
    Asch, J., Bourget, O., Joye, A.: Localization properties of the Chalker-Coddington model. Ann. Henri Poincaré 11, 1341–1373 (2010) MathSciNetADSzbMATHCrossRefGoogle Scholar
  5. 5.
    Asch, J., Meresse, C.: A constant of quantum motion in two dimensions in crossed magnetic and electric fields. J. Phys. A, Math. Theor. 43, 474002 (2010) MathSciNetADSCrossRefGoogle Scholar
  6. 6.
    Chalker, J.T., Coddington, P.D.: Percolation, quantum tunneling and the integer Hall effect. J. Phys. C 21, 2665–2679 (1988) ADSCrossRefGoogle Scholar
  7. 7.
    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) ADSzbMATHCrossRefGoogle Scholar
  8. 8.
    Hamza, E., Joye, A., Stolz, G.: Dynamical localization for unitary Anderson models. Math. Phys. Anal. Geom. 12(4), 381–444 (2009) MathSciNetzbMATHCrossRefGoogle Scholar
  9. 9.
    Joye, A.: Fractional moment estimates for random unitary operators. Lett. Math. Phys. 72, 51–64 (2005) MathSciNetADSzbMATHCrossRefGoogle Scholar
  10. 10.
    Klein, A.: Extended states in the Anderson model on the Bethe lattice. Adv. Math. 133, 163–184 (1998) MathSciNetzbMATHCrossRefGoogle Scholar
  11. 11.
    Kramer, B., Ohtsuki, T., Kettemann, S.: Random network models and quantum phase transitions in two dimensions. Phys. Rep. 417, 211–342 (2005) MathSciNetADSCrossRefGoogle Scholar
  12. 12.
    Stollmann, P.: Caught by disorder. In: Bound States in Random Media. Progress in Mathematical Physics, vol. 20. Birkhäuser, Boston (2001) Google Scholar
  13. 13.
    Trugman, S.A.: Localization, percolation, and the quantum Hall effect. Phys. Rev. B 27, 7539–7546 (1983) ADSCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  1. 1.CPTAix-Marseille Univ.Marseille cedex 9France
  2. 2.CNRS, UMR 7332Marseille cedex 9France
  3. 3.CPTUniv. Sud Toulon VarLa GardeFrance
  4. 4.Departamento de MatemáticasPontificia Universidad Católica de ChileMacul SantiagoChile
  5. 5.UMR 5582, CNRS Institut FourierUJF-Grenoble 1GrenobleFrance

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