Pumping of charge (Q) in a closed ring geometry is not quantized even in thestrict adiabatic limit. The deviation form exact quantization can be related tothe Thouless conductance. We use Kubo formalism as a starting point for thecalculation of both the dissipative and the adiabatic contributions to Q. As anapplication we bring examples for classical dissipative pumping, classicaladiabatic pumping, and in particular we make an explicit calculation forquantum pumping in case of the simplest pumping device, which is a 3 sitelattice model.
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