Anderson localization for a two-dimensional rotor

Abstract

A two-dimensional generalization of the one-dimensional kicked-rotor model is introduced. As in one dimension, this model can be mapped on a two-dimensional Anderson model for localization. It is found that all the states are localized in momentum space and that the localization length grows exponentially with the mean free path, as expected from the scaling theory for localization. This suggests that the correspondence between the quantum dynamics of chaotic systems and Anderson localization that was found in one dimension holds in two dimensions as well.