  In this paper we present generic properties of quantum transport in
mono-layer graphene. In the scheme of the Kubo-Geenwood formula, we compute the
square spreading of wave packets of a given energy with is directly related to
conductivity. As a first result, we compute analytically the time dependent
diffusion for pure graphene. In addition to the semi-classical term a second
term exists that is due to matrix elements of the velocity operator between
electron and hole bands. This term is related to velocity fluctuations i.e.
Zitterbewegung effect. Secondly, we study numerically the quantum diffusion in
graphene with simple vacancies and pair of neighboring vacancies (divacancies),
that simulate schematically oxidation, hydrogenation and other
functionalisations of graphene. We analyze in particular the time dependence of
the diffusion and its dependence on energy in relation with the electronic
structure. We compute also the mean free path and the semi-classical value of
the conductivity as a function of energy in the limit of small concentration of
defects.
