Re-localization due to finite response times in a nonlinear Anderson chain

  • M. Mulansky
  • A. S. Pikovsky
Regular Article


We study a disordered nonlinear Schrödinger equation with an additional relaxation process having a finite response time τ. Without the relaxation term, τ = 0, this model has been widely studied in the past and numerical simulations showed subdiffusive spreading of initially localized excitations. However, recently Caetano et al. [Eur. Phys. J. B 80, 321 (2011)] found that by introducing a response time τ > 0, spreading is suppressed and any initially localized excitation will remain localized. Here, we explain the lack of subdiffusive spreading for τ > 0 by numerically analyzing the energy evolution. We find that in the presence of a relaxation process the energy drifts towards the band edge, which enforces the population of fewer and fewer localized modes and hence leads to re-localization. The explanation presented here relies on former findings by Mulansky et al. [Phys. Rev. E 80, 056212 (2009)] on the energy dependence of thermalized states.


Solid State and Materials 


  1. 1.
    R.A. Caetano, F.A.B.F. de Moura, M.L. Lyra, Eur. Phys. J. B 80, 321 (2011)MathSciNetADSCrossRefGoogle Scholar
  2. 2.
    M. Mulansky, K. Ahnert, A.S. Pikovsky, D.L. Shepelyansky, Phys. Rev. E 80, 056212 (2009)ADSCrossRefGoogle Scholar
  3. 3.
    P.W. Anderson, Phys. Rev. 109, 1492 (1958)ADSCrossRefGoogle Scholar
  4. 4.
    A.S. Pikovsky, D.L. Shepelyansky, Phys. Rev. Lett. 100, 094101 (2008)ADSCrossRefGoogle Scholar
  5. 5.
    T. Schwartz, G. Bartal, S. Fishman, M. Segev, Nature 446, 52 (2007)ADSCrossRefGoogle Scholar
  6. 6.
    B. Deissler et al., Nature Phys. 6, 354 (2010)ADSCrossRefGoogle Scholar
  7. 7.
    D.M. Basko, Ann. Phys. 326, 1577 (2011)MathSciNetADSzbMATHCrossRefGoogle Scholar
  8. 8.
    S. Flach, D.O. Krimer, Ch. Skokos, Phys. Rev. Lett. 102, 24101 (2009)ADSCrossRefGoogle Scholar
  9. 9.
    M. Mulansky, A.S. Pikovsky, Europhys. Lett. 90, 10015 (2010)ADSCrossRefGoogle Scholar
  10. 10.
    M. Mulansky, K. Ahnert, A.S. Pikovsky, D.L. Shepelyansky, J. Stat. Phys. 145, 1256 (2011)ADSzbMATHCrossRefGoogle Scholar
  11. 11.
    M. Mulansky, K. Ahnert, A.S. Pikovsky, Phys. Rev. E 83, 026205 (2011)ADSCrossRefGoogle Scholar
  12. 12.
    D.L. Shepelyansky, Phys. Rev. Lett. 70, 1787 (1993)ADSCrossRefGoogle Scholar
  13. 13.
    P.A. Lee, T.V. Ramakrishnan, Rev. Mod. Phys. 57, 287 (1985)ADSCrossRefGoogle Scholar
  14. 14.
    K. Ahnert, M. Mulansky, AIP Conf. Proc. 1389, 1586 (2011)ADSCrossRefGoogle Scholar
  15. 15.
    G. Kopidakis, S. Komineas, S. Flach, S. Aubry, Phys. Rev. Lett. 100, 084103 (2008)ADSCrossRefGoogle Scholar

Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.Department of Physics and AstronomyPotsdam UniversityPotsdamGermany

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