  Observable effects due to trembling motion (Zitterbewegung, ZB) of charge
carriers in bilayer graphene, monolayer graphene and carbon nanotubes are
calculated. It is shown that, when the charge carriers are prepared in the form
of gaussian wave packets, the ZB has a transient character with the decay time
of femtoseconds in graphene and picoseconds in nanotubes. Analytical results
for bilayer graphene allow us to investigate phenomena which accompany the
trembling motion. In particular, it is shown that the transient character of ZB
in graphene is due to the fact that wave subpackets related to positive and
negative electron energies move in opposite directions, so their overlap
diminishes with time. This behavior is analogous to that of the wave packets
representing relativistic electrons in a vacuum.
