  We consider Dirac quasi-particles, as realized with cold atoms loaded in a
honeycomb lattice or in a $\pi$-flux square lattice, in the presence of a weak
correlated disorder such that the disorder fluctuations do not couple the two
Dirac points of the lattices. We numerically and theoretically investigate the
time evolution of the momentum distribution of such quasi-particles when they
are initially prepared in a quasi-monochromatic wave packet with a given mean
momentum. The parallel transport of the pseudo-spin degree of freedom along
scattering paths in momentum space generates a geometrical phase which alters
the interference associated with reciprocal scattering paths. In the massless
case, a well-known dip in the momentum distribution develops at backscattering
(respective to the Dirac point considered) around the transport mean free time.
This dip later vanishes in the honeycomb case because of trigonal warping. In
the massive case, the dynamical phase of the scattering paths becomes crucial.
Its interplay with the geometrical phase induces an additional transient broken
reflection symmetry in the momentum distribution. The direction of this
asymmetry is a property of the Dirac point considered, independent of the
energy of the wave packet. These Berry phase effects could be observed in
current cold atom lattice experiments.
