Equation of motion approach to non-adiabatic quantum charge pumping

We use the equations of motion of non-interacting electrons in a one-dimensional system to numerically study different aspects of charge pumping. We study the effects of the pumping frequency, amplitude, band filling and finite bias on the charge pumped per cycle, and the Fourier transforms of the charge and energy currents in the leads. Our method works for all values of parameters, and gives the complete time dependences of the current and charge at any site of the system. Our results agree with Floquet and adiabatic scattering theory where these are applicable, and provides support for a mechanism proposed elsewhere for charge pumping by a travelling potential wave. For non-adiabatic and strong pumping, the charge and energy currents are found to have a marked asymmetry between the two leads, and pumping can work even against a substantial bias.