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

  • We study a disordered nonlinear Schrodinger equation with an additional relaxation process having a finite response time tau. Without the relaxation term, tau = 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 tau > 0, spreading is suppressed and any initially localized excitation will remain localized. Here, we explain the lack of subdiffusive spreading for tau > 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.

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Author:Mario Mulansky, Arkady S. Picovsky
ISSN:1434-6028 (print)
Parent Title (English):The European physical journal : B, Condensed matter and complex systems
Place of publication:New York
Document Type:Article
Year of first Publication:2012
Year of Completion:2012
Release Date:2017/03/26
Organizational units:Mathematisch-Naturwissenschaftliche Fakultät / Institut für Physik und Astronomie
Peer Review:Referiert