Anderson Localization For The Quantum Kicked Rotor Model

TL;DR

This paper proves Anderson localization for the quantum kicked rotor model, demonstrating that it has pure point spectrum with exponentially decaying eigenfunctions under certain conditions, advancing understanding of quantum chaos and localization phenomena.

Contribution

It establishes Anderson localization for the quantum kicked rotor model with a rigorous proof of pure point spectrum and exponential decay of eigenfunctions.

Findings

Proved Anderson localization for the quantum kicked rotor model.

Demonstrated pure point spectrum with exponentially decaying eigenfunctions.

Applicable for almost all Diophantine frequencies.

Abstract

In this paper, we establish Anderson localization for the quantum kicked rotor model. More precisely, we proved that \begin{equation*} H=\tan\pi\left(x_0+my_0+\frac{m(m-1)}{2}\omega\right) \delta_{mn}+\epsilon S_\phi \end{equation*} has pure point spectrum with exponentially decaying eigenfunctions for almost all $\omega \in DC$ (diophantine condition).