Abstract: Quantum pumps are devices (for example realized as quantum dots) generating currents between two or more leads as a result of being operated parametrically. We introduce a mathematical setup for charge transport in quantum pumps and consider the pumped current in the adiabatic limit, and in the limit where its measurement is done deep within a lead. It is proven that under rather general assumptions on the Hamiltonian describing the system, that current is given by a formula of Büttiker, Prêtre and Thomas, relating it to the frozen $S$-matrix and it s time derivative.

This result is based on joint work with J.Avron, A.Elgart, G.M. Graf, and L.Sadun.