  We investigate the classical chaotic diffusion of atoms subjected to {\em
pairs} of closely spaced pulses (`kicks) from standing waves of light (the
$2\delta$-KP). Recent experimental studies with cold atoms implied an
underlying classical diffusion of type very different from the well-known
paradigm of Hamiltonian chaos, the Standard Map.
  The kicks in each pair are separated by a small time interval $\epsilon \ll
1$, which together with the kick strength $K$, characterizes the transport.
Phase space for the $2\delta$-KP is partitioned into momentum `cells' partially
separated by momentum-trapping regions where diffusion is slow. We present here
an analytical derivation of the classical diffusion for a $2\delta$-KP
including all important correlations which were used to analyze the
experimental data.
  We find a new asymptotic ($t \to \infty$) regime of `hindered' diffusion:
while for the Standard Map the diffusion rate, for $K \gg 1$, $D \sim K^2/2[1-
J_2(K)..]$ oscillates about the uncorrelated, rate $D_0 =K^2/2$, we find
analytically, that the $2\delta$-KP can equal, but never diffuses faster than,
a random walk rate.
  We argue this is due to the destruction of the important classical
`accelerator modes' of the Standard Map.
  We analyze the experimental regime $0.1\lesssim K\epsilon \lesssim 1$, where
quantum localisation lengths $L \sim \hbar^{-0.75}$ are affected by fractal
cell boundaries. We find an approximate asymptotic diffusion rate $D\propto
K^3\epsilon$, in correspondence to a $D\propto K^3$ regime in the Standard Map
associated with 'golden-ratio' cantori.
