Eur. Phys. J. B (2012) 85: 105
https://doi.org/10.1140/epjb/e2012-21040-5

Regular Article

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

Department of Physics and Astronomy, Potsdam University, 14476 Potsdam, Germany

^a e-mail: mulansky@uni-potsdam.de

Received: 16 December 2011
Received in final form: 2 February 2012
Published online: 26 March 2012

Abstract

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.