What is Quantum in Quantum Pumping: The Role of Phase and Asymmetries
  We show that quantum pumping does not always require a quantum description or a quantum phase. Quantum pumping is shown to encompass different types of processes, some of which intrinsically rely on phase while others do not. We also show that many pumping processes have a hidden antisymmetric component that contributes significantly to the instantaneous current at the terminals without causing net charge transfer in a period. We have also computed the exact pumped current for some cases over a full range of time variation from adiabatic to non-adiabatic. 
Kunal K. Das, and Tomas Opatrny