Two distinct ballistic processes in graphene

A dynamical approach to ballistic transport in mesoscopic graphene samples of finite length Land contact potential difference with leads U is developed. It is shown that at ballistic times shorter than both relevant time scales, t _L = L/v_g (v_g - Fermi velocity) and t _u = H/(eU), the major effect of electric field is to creates the electron - hole pairs, namely causes interband transitions. At ballistic times lager than the two scales the mechanism is very different. The conductivity has its "nonrelativistic" or intraband value equal to the one obtained within the Landauer-Butticker approach for the barrier Uresulting from evanescent waves tunneling through the barrier.