  The quantum dynamics of atoms subjected to pairs of closely-spaced
$\delta$-kicks from optical potentials are shown to be quite different from the
well-known paradigm of quantum chaos, the singly-$\delta$-kicked system. We
find the unitary matrix has a new oscillating band structure corresponding to a
cellular structure of phase-space and observe a spectral signature of a
localization-delocalization transition from one cell to several. We find that
the eigenstates have localization lengths which scale with a fractional power
$L \sim \hbar^{-.75}$ and obtain a regime of near-linear spectral variances
which approximate the `critical statistics' relation $\Sigma_2(L) \simeq \chi L
\approx {1/2}(1-\nu) L$, where $\nu \approx 0.75$ is related to the fractal
classical phase-space structure. The origin of the $\nu \approx 0.75$ exponent
is analyzed.
