We consider Dirac quasi-particles, as realized with cold atoms loaded in a honeycomb lattice or in a π-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.PACS numbers: 42.25. Dd, 37.10.Jk, 03.65.Vf, Introduction.-Topology and gauge fields, as exemplified by Chern numbers [1], Berry phases and curvatures [2], are key concepts at the heart of many condensed-matter phenomena [3,4]. One main reason is that Bloch's theorem introduces wave numbers k belonging to a parameter space with the topology of a torus, the Brillouin zone, and a set of periodic wave functions depending parametrically on k. Together they offer natural settings for bundles and connections [5]. With the recent advances in the generation of synthetic magnetic fields [6][7][8] and the ability to load independent or interacting bosons and/or fermions into two-dimensional optical lattices [9][10][11] where the relevant experimental parameters are perfectly under control, ultracold atoms have become versatile tools to explore directions borrowed from other fields like topological defects [12], color superfluidity [13], engineering and measuring non-zero momentum-space Berry curvatures [14] or creating quantum Hall states with strong effective magnetic fields [15][16][17][18].In this work, we consider the momentum space dynamics of Dirac quasi-particles [19][20][21], as found for example in graphene sheets, in the presence of a correlated and weak on-site disorder. A semi-classical approach shows that the dynamics of these quasi-particles is unaffected by the topology of the band structure as long as a net effective electric field is absent [4,22]. We go beyond this semi-classical approach to address the competition happening at short times between Berry phase effects induced by the Bloch states topology and dynamical coherent corrections to transport due to the interference associa...