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1988•Physical Review LettersRequires access

Anderson localization for a two-dimensional rotor

E. Doron, Shmuel Fishman

Open publisher page 56 citations

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.

About this research paper

What this paper is about

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.

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OpenAlex reports 56 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available 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.

Key concepts: Anderson localization, Dimension (graph theory), Anderson impurity model, Physics, Scaling, Generalization, Weak localization, Space (punctuation)

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