  Previous work [Gong and Brumer, Phys. Rev. Lett., 97, 240602 (2006)]
motivates this study as to how asymmetry-driven quantum ratchet effects can
persist despite a corresponding fully chaotic classical phase space. A simple
perspective of ratchet dynamics, based on the Heisenberg picture, is
introduced. We show that ratchet effects are in principle of common origin in
classical and quantum mechanics, though full chaos suppresses these effects in
the former but not necessarily the latter. The relationship between ratchet
effects and coherent dynamical control is noted.
