  We examine the effect of the initial atomic momentum distribution on the
dynamics of the atom-optical realisation of the quantum kicked rotor. The atoms
are kicked by a pulsed optical lattice, the periodicity of which implies that
quasi-momentum is conserved in the transport problem. We study and compare
experimentally and theoretically two resonant limits of the kicked rotor: in
the vicinity of the quantum resonances and in the semiclassical limit of
vanishing kicking period. It is found that for the same experimental
distribution of quasi-momenta, significant deviations from the kicked rotor
model are induced close to quantum resonance, while close to the classical
resonance (i.e. for small kicking period) the effect of the quasi-momentum
vanishes.
