  We study directed transport in periodically forced scattering systems in the
regime of fast and strong driving where the dynamics is mixed to chaotic and
adiabatic approximations do not apply. The model employed is a square potential
well undergoing lateral oscillations, alternatively as two- or single-parameter
driving. Mechanisms of directed transport are analyzed in terms of asymmetric
irregular scattering processes. Quantizing the system in the framework of
Floquet scattering theory, we calculate directed currents on basis of
transmission and reflection probabilities obtained by numerical wavepacket
scattering. We observe classical as well as quantum transport beyond linear
response, manifest in particular in a non-zero current for single-parameter
driving where according to adiabatic theory, it should vanish identically.
