Eur. Phys. J. B 80, 321-324 (2011)
https://doi.org/10.1140/epjb/e2011-20006-5

Anderson localization in a disordered chain with a finite nonlinear response time

Instituto de Física, Universidade Federal de Alagoas, 57072-970 Maceió, AL, Brazil

Corresponding author: ^a fidelis@if.ufal.br

Received: 6 January 2011
Revised: 4 February 2011
Published online: 14 March 2011

Abstract

In this work, we investigate the competition of disorder, nonlinearity and non-adiabatic process on the wave packet dynamics in 1D. We follow the time evolution of the second moment of the wave packet distribution to characterize its spreading behavior. In order to describe the dynamical behavior of one-electron wave packets, we solve a discrete nonlinear Schrödinger equation which effectively takes into account a diagonal disorder and a nonlinear contribution. Going beyond the adiabatic regime, we consider that the nonlinearity relaxes in time according to a Debye-like law. In the adiabatic regime, it has been recently demonstrated that the interplay of disorder and nonlinearity leads to a sub-diffusive spread of the wave packet. Here, we numerically demonstrate that no sub-diffusive spreading of the second moment of the wave packet distribution takes place when the finite response time of the nonlinearity is taken into account.