  At low temperatures and strong friction the time evolution of the density
distribution in position follows a quantum Smoluchowski equation. Recently,
also higher-order contributions of quantum fluctuations to drift and diffusion
coefficients have been systematically derived. As a non-trivial situation to
reveal the impact of subleading quantum corrections and to demonstrate
convergence properties of the perturbation series, directed transport in
ratchets is studied. It is shown that the perturbation series typically has a
non-monotonous behavior. Depending on symmetry properties higher order
contributions may even compensate current reversals induced by leading quantum
fluctuations. This analysis demonstrates how to consistently treat the dynamics
of overdamped quantum systems at low temperatures also in numerical
applications.
