  We study classical and quantum dynamics of a kicked relativistic particle
confined in a one dimensional box. It is found that in classical case for
chaotic motion the average kinetic energy grows in time, while for mixed regime
the growth is suppressed. However, in case of regular motion energy fluctuates
around certain value. Quantum dynamics is treated by solving the time-dependent
Dirac equation for delta-kicking potential, whose exact solution is obtained
for single kicking period. In quantum case, depending on the values of the
kicking parameters the average kinetic energy can be quasi periodic or,
fluctuating around some value. Particle transport is studied by considering
spatio-temporal evolution of the Gaussian wave packet and by analyzing
trembling motion.
