  Directed classical current that increases linearly with time without using a
biased external field is obtained in a simple model Hamiltonian system derived
from a modified kicked rotor model, by breaking the spatial symmetry of the
transporting regular islands in the classical phase space. A parallel study of
the corresponding quantum dynamics suggests that although quantum coherence
effects suppress the directed current and can even induce a current reversal,
directed quantum current that increases linearly with time can nonetheless be
realized in a quantum system that is far from the classical limit.
