Dynamical Localization and Delocalization in Polychromatically Perturbed Anderson Map

Abstract

In the previous paper [PRE 101,032210(2020)], localization and delocalization phenomena in the polychromatically perturbed Anderson map (AM) were elucidated mainly from the viewpoint of localization-delocalization transition (LDT) on the increase of the perturbation strength $\epsilon$. In this paper, we mainly investigate the dependency of the phenomena on the disorder strength $W$ ($W-$dependence) in the AM with a characteristic disorder strength $W^{\ast }$. In the completely localized region the $W-$dependence and $\epsilon -$dependence of the localization length show characteristic behavior similar to those reported in monochromatically perturbed case [PRE 97,012210(2018)]. Furthermore, the obtained results show that even for the increase of the $W$, the critical phenomena and critical exponent are found to be similar to those in the LDT caused by the increase of $\epsilon$. We also investigate the diffusive properties of the delocalized states induced by the parameters.

12 pages, 15 figures