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Quantum pumping through mesoscopic quantum dots is known to be enhanced byresonant transmission. The pumped charge is close to an integer number ofelectrons when the pumping contour surrounds a resonance, but the transmissionremains small on the contour. For non-interacting electrons, we give aquantitative account of the detailed exchange of electrons between the dot andthe leads (to the electron reservoirs) during a pumping cycle. Near isolateddistinct resonances, we use approximate Breit-Wigner expressions for the dot'sGreen function to discuss the loading/unloading picture of the pumping: thefractional charge exchanged between the dot and each lead through a singleresonance point is related to the relative couplings of the dot and the leadsat this resonance. If each resonance point along the pumping contour isdominated by the coupling to a single lead (which also implies a very smalltransmission), then the crossing of each such resonance results in a singleelectron exchange between the dot and that lead, ending up with a net quantizedcharge. When the resonance approximation is valid, the fractional charges canalso be extracted from the peaks of the transmissions between the variousleads.Comment: 10 pages, 4 figure

Resonance approximation and charge loading and unloading in adiabatic quantum pumping