  The dynamical approach is applied to ballistic transport in mesoscopic
graphene samples of length L and contact potential U. At times shorter than
both relevant time scales, the flight time and \hslash/U, the major effect of
the electric field is to create electron - hole pairs, i.e. causing interband
transitions. In linear response this leads (for width W>>L) to conductivity
pi/2 e^{2}/h. On the other hand, at times lager than the two scales the
mechanism and value are different. It is shown that the conductivity approaches
its intraband value, equal to the one obtained within the Landauer-Butticker
approach resulting from evanescent waves. It is equal to 4/pi e^{2}/h for W>>L.
The interband transitions, within linear response, are unimportant in this
limit. Between these extremes there is a crossover behaviour dependent on the
ratio between the two time scales. At strong electric fields (beyond linear
reponse) the interband process dominates. The electron-hole mechanism is
universal, namely does not depend on geometry (aspect ratio, topology of
boundary conditions, properties of leads), while the evanescent modes mechanism
depends on all of them. On basis of the results we determine, that while in
absorption measurements and in DC transport in suspended graphene the first
conductivity value was measured, the latter one would appear in experiments on
small ballistic graphene flakes on substrate.
