  We present an analytic theory of quantum interference and Anderson
localization in the quantum kicked rotor (QKR). The behavior of the system is
known to depend sensitively on the value of its effective Planck's constant
$\he$. We here show that for rational values of $\he/(4\pi)=p/q$, it bears
similarity to a disordered metallic ring of circumference $q$ and threaded by
an Aharonov-Bohm flux. Building on that correspondence, we obtain quantitative
results for the time--dependent behavior of the QKR kinetic energy, $E(\tilde
t)$ (this is an observable which sensitively probes the system's localization
properties). For values of $q$ smaller than the localization length $\xi$, we
obtain scaling $E(\tilde t) \sim \Delta \tilde t^2$, where $\Delta=2\pi/q$ is
the quasi--energy level spacing on the ring. This scaling is indicative of a
long time dynamics that is neither localized nor diffusive. For larger values
$q\gg \xi$, the functions $E(\tilde t)\to \xi^2$ saturates (up to exponentially
small corrections $\sim\exp(-q/\xi)$), thus reflecting essentially localized
behavior.
