Re-localization due to finite response times in a nonlinear Anderson chain
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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.
KeywordsSolid State and Materials