Pumping current in a non-Markovian N-state model

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