  During an adiabatic pumping cycle a conventional two barrier quantum device
takes an electron from the left lead and ejects it to the right lead. Hence the
pumped charge per cycle is naively expected to be $Q \le e$. This zero order
adiabatic point of view is in fact misleading. For a closed device we can get
${Q > e}$ and even ${Q \gg e}$. In this paper a detailed analysis of the
quantum pump operation is presented. Using the Kubo formula for the geometric
conductance, and applying the Dirac chains picture, we derive practical
estimates for~$Q$.
