  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).
