  We revisit the problem of diffusion in a driven system consisting of an
inertial Brownian particle moving in a symmetric periodic potential and
subjected to a symmetric time-periodic force. We reveal parameter domains in
which diffusion is normal in the long time limit and exhibits intriguing giant
damped quasiperiodic oscillations as a function of the external driving
amplitude. As the mechanism behind this effect we identify the corresponding
oscillations of difference in the number of locked and running trajectories
which carries the leading contribution to the diffusion coefficient. Our
findings can be verified experimentally in a multitude of physical systems
including colloidal particles, Josephson junction or cold atoms dwelling in
optical lattices, to name only a few.
