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A periodically modulated N-state model whose dynamics is governed by atime-convoluted generalized master equation is theoretically analyzed. It isshown that this non-Markovian master equation can be converted to a Markovianmaster equation having a larger transition matrix, which affords easieranalysis. The behavior of this model is investigated by focusing on thecycle-averaged pumping current. In the adiabatic limit, the geometrical currentis calculated analytically, and compared to numerical results which areavailable for a wide range of modulation frequencies.

Pumping current in a non-Markovian $N$-state model