Adiabatic charge pumping in open quantum systems
  We introduce a mathematical setup for charge transport in quantum pump connected to a number of external leads. It is proved that under rather general assumption on the Hamiltonian describing the system, in the adiabatic limit, the current through the pump is given by a formula of Buttiker, Pretre, and Thomas, relating it to the frozen S-matrix and its time derivative. 
J.E. Avron, A. Elgart, G.M. Graf, L. Sadun, K. Schnee