Classical diffusive dynamics for the quasiperiodic kicked rotor

TL;DR

This paper investigates the classical dynamics of a quasiperiodic kicked rotor, demonstrating that it exhibits 3D anisotropic diffusion, which supports its connection to the quantum Anderson transition observed experimentally.

Contribution

It provides analytical predictions for the diffusion tensor in the classical quasiperiodic kicked rotor and confirms them with numerical simulations, clarifying its chaotic behavior.

Findings

Classical dynamics is 3D anisotropic diffusion.

Analytical diffusion tensor matches numerical results.

Supports the classical-quantum correspondence in Anderson transition.

Abstract

We study the classical dynamics of a quasiperiodic kicked rotor, whose quantum counterpart is known to be an equivalent of the 3D Anderson model. Using this correspondence allowed for a recent experimental observation of the Anderson transition with atomic matter waves. In such a context, it is particularly important to assert the chaotic character of the classical dynamics of this system. We show here that it is a 3D anisotropic diffusion. Our simple analytical predictions for the associated diffusion tensor are found in good agreement with the results of numerical simulations.