  Quantum pumping through mesoscopic quantum dots is known to be enhanced by
resonant transmission. The pumped charge is close to an integer number of
electrons when the pumping contour surrounds a resonance, but the transmission
remains small on the contour. For non-interacting electrons, we give a
quantitative account of the detailed exchange of electrons between the dot and
the leads (to the electron reservoirs) during a pumping cycle. Near isolated
distinct resonances, we use approximate Breit-Wigner expressions for the dot's
Green function to discuss the loading/unloading picture of the pumping: the
fractional charge exchanged between the dot and each lead through a single
resonance point is related to the relative couplings of the dot and the leads
at this resonance. If each resonance point along the pumping contour is
dominated by the coupling to a single lead (which also implies a very small
transmission), then the crossing of each such resonance results in a single
electron exchange between the dot and that lead, ending up with a net quantized
charge. When the resonance approximation is valid, the fractional charges can
also be extracted from the peaks of the transmissions between the various
leads.
