  The quantum kicked rotor (QKR) driven by $d$ incommensurate frequencies
realizes the universality class of $d$-dimensional disordered metals. For
$d>3$, the system exhibits an Anderson metal-insulator transition which has
been observed within the framework of an atom optics realization. However, the
absence of genuine randomness in the QKR reflects in critical phenomena beyond
those of the Anderson universality class. Specifically, the system shows strong
sensitivity to the algebraic properties of its effective Planck constant
$\tilde h \equiv 4\pi /q$. For integer $q$, the system may be in a globally
integrable state, in a `super-metallic' configuration characterized by
diverging response coefficients, Anderson localized, metallic, or exhibit
transitions between these phases. We present numerical data for different
$q$-values and effective dimensionalities, with the focus being on parameter
configurations which may be accessible to experimental investigations.
