Anderson Localization For The Quantum Kicked Rotor Model

Abstract

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

arXiv admin note: text overlap with arXiv:1909.06542 and arXiv:1908.00229