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.
Author details: | Mario Mulansky, Arkady S. Picovsky |
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DOI: | https://doi.org/10.1140/epjb/e2012-21040-5 |
ISSN: | 1434-6028 |
Title of parent work (English): | The European physical journal : B, Condensed matter and complex systems |
Publisher: | Springer |
Place of publishing: | New York |
Publication type: | Article |
Language: | English |
Year of first publication: | 2012 |
Publication year: | 2012 |
Release date: | 2017/03/26 |
Volume: | 85 |
Issue: | 3 |
Number of pages: | 3 |
Organizational units: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Physik und Astronomie |
Peer review: | Referiert |