Scaling Properties of Dynamical Localization in Monochromatically Perturbed Quantum Maps: standard map and Anderson map

TL;DR

This paper investigates dynamical localization in perturbed quantum maps, proposing phenomenological formulas for localization length, confirming a new localization regime in Anderson map, and connecting results to self-consistent mean-field theory.

Contribution

It introduces new phenomenological formulas for localization length in quantum maps and confirms a novel localization regime in Anderson map through numerical analysis.

Findings

Phenomenological formula matches experimental data for standard map.

Confirmation of a new localization regime in Anderson map.

Discussion of transient diffusion in large localization length limit.

Abstract

Dynamical localization phenomena of monochromatically perturbed standard map (SM) and Anderson map (AM), which are both identified with a two-dimensional disordered system under suitable conditions, are investigated by the numerical wavepacket propagation. Some phenomenological formula of the dynamical localization length valid for wide range of control parameters are proposed for both SM and AM. For SM the formula completely agree with the experimentally established formula, and for AM the presence of a new regime of localization is confirmed. These formula can be derived by the self-consistent mean-field theory of Anderson localization on the basis of a new hypothesis for cut-off length. Transient diffusion in the large limit of the localization length is also discussed.