  We report an experimental and theoretical study of the dynamics of cold atoms
subjected to closely-spaced pairs of pulses in an optical lattice. The
experiments show the interplay between fully coherent quantum dynamics and a
novel momentum-diffusion regime: for all previously-studied delta-kicked
systems, chaotic classical dynamics shows diffusion with short-time (2 or
3-kick) correlations; here, chaotic diffusion combines with new types of
long-ranged 'global' correlations, between all kick-pairs, which control
transport through trapping regions in phase-space. Analytical formulae are
presented and, with quantum localization, are used to analyse the experiments.
