Nonadiabatic effect in a quantum charge pump

Nonadiabatic effects in a quantum charge pump are studied through the exact solution of a time-dependent Schrödinger equation and the noninteracting Anderson impurity model. An approximate solution to the interacting Anderson model in the large Coulomb repulsion limit is also presented. The nonadiabatic corrections are rigorously found to die off exponentially as the pumping frequency goes to zero. Moreover, the semiclassical rate equation is derived when the temperature is higher than the energy quantum of the pumping frequency. Finally, nonadiabatic heating in the system is discussed.