Abstract
A periodically modulated N-state model whose dynamics is 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 to numerical results which are available for a wide range of modulation frequencies.
Highlights
Master equations (MEs) are widely used in nonequilibrium statistical mechanics to model the time evolution of a range of classical and quantum-mechanical systems
It was shown that the nonMarkovian SN model, governed by a non-Markovian master equation, which includes a time-convolution integral, can be converted to a larger Markovian system, which is easier to analyze
A method of solving the system dynamics, at least numerically without needing to resort to any perturbative expansions, was presented, yielding an approach to deal with this type of non-Markovian ME (nMME), which is in principle exact
Summary
Master equations (MEs) are widely used in nonequilibrium statistical mechanics to model the time evolution of a range of classical and quantum-mechanical systems. The mathematical foundation of MEs is the differential Chapman-Kolmogorov equation of stochastic analysis [1], and in its basic form, it only describes systems that carry no memory of their past; this property is referred to as Markovianity. It is known, that due to a number of physical reasons, real systems do usually possess some degree of memory of their past evolution and obey a non-Markovian ME (nMME). Advancements in experimental techniques have made it possible to directly measure non-Markovianity in the context of classical [8] and quantum [9,10] systems
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